The importance of special relativistic effects in modelling ultra-fast outflows

Abstract

Context. Outflows are observed in a variety of astrophysical sources. Remarkably, ultra-fast (v ≥ 0.1c), highly ionised outflows in the UV and X-ray bands are often seen in Active Galactic Nuclei (AGNs). Depending on their kinetic power and mass outflow rate, respectivelyĖ out ,Ṁ out , such outflows may play a key role in regulating the AGN-host galaxy co-evolution process through cosmic time and metal-feeding the surrounding CGM/IGM. It is therefore crucial to provide accurate estimates of the wind properties, includinġ M out ,Ė out . Aims. Here, we concentrate on special relativistic effects concerning the interaction of light with matter moving at relativistic speed relatively to the source of radiation. Our aim is to assess the impact of these effects on the observed properties of the outflows and implement a correction for these effects in the existing spectral modelling routines. Methods. We define a simple procedure to incorporate relativistic effects in radiative transfer codes. Following this procedure, we run a series of simulations to explore the impact of relativistic effects for different outflow velocities and column densities. Results. The observed optical depth of the wind is usually considered a proxy for its column density N H , independently on the velocity of the outflow. However, our simulations show that the observed optical depth of an outflow with a given column density N H decreases rapidly as the velocity of the wind approaches relativistic values. This, in turn, implies that when estimating N H from the optical depth, it is necessary to include a velocity-dependent correction, already for moderate velocities (e.g. v out > ∼ 0.05c). This correction linearly propagates to the derived quantitiesṀ out ,Ė out . Conclusions. We demonstrate that special relativistic effects must be considered in order to obtain correct estimates ofṀ out anḋ E out for an outflow moving at mildly relativistic speed relatively to the illuminating source of radiation. As an example we calculate the relativistically corrected values ofṀ out andĖ out for a sample of ∼ 30 Ultra-Fast Outflows (UFOs) taken from the literature and find correction factors of 20 − 120% within the observed range of outflowing velocities (v out ≈ 0.1 − 0.3c). This brings the ratio betweenṀ out and the disk accretion rate close or even above unity for the vast majority of the sources of the sample, highlighting the importance of the reported relativistic corrections to understand the growth of the most massive black holes. The upcoming next generation of high sensitivity X-ray telescopes such as XRISM and Athena will provide a much more complete census of UFOs, especially in the fastest velocity regime where the relativistic corrections are increasingly important.

Ionized outflows from active galactic nuclei as the essential elements of feedback

“…Certain preliminary results point out that dramatic changes in the flow pattern does not necessary translate to significant changes in the predicted spectra (see for example, Moscibrodzka et al 2007;Waters et al 2017), however, more work needs to be done. Similarly, the special relativistic effects in simulating AGN outflows need to be considered (Sim et al 2010;Luminari et al 2020).…”

Location and energetics of the ultra-fast outflow in PG 1448+273

“…For each slab, we derived the ionization parameter at its inner edge as ξ(r i ) = L i /n(r i )r 2 i . Importantly, we also included special relativistic effects, following the procedure outlined in Luminari et al (2020). We used as outflowing velocity v out = v(r ), where r is the mass-averaged radial coordinate of the slab and is comprised of r i and r e .…”

Qwind3: UV line-driven accretion disc wind models for AGN feedback

“…This is explained in detail in section 5. Lastly, we include the relativistic corrections from Luminari et al (2020) in the calculation of the radiation force, solving the issue of superluminal winds, and we later compare our findings to Luminari et al (2021). Readers interested only in the results should skip to Section 9.…”

“…When the gas trajectory approaches the speed of light, one should consider special relativistic effects such as relativistic beaming and Doppler shifting (see eg Rybicki & Lightman 1986, chapter 4). The importance of taking these effects into account is highlighted in Luminari et al (2020). We include a correction to the radiation flux seen by the gas (Equation 4),…”