Improved measurements of turbulence in the hot gaseous atmospheres of nearby giant elliptical galaxies

TL;DR

This study provides improved measurements of turbulence in the hot gas halos of nearby giant elliptical galaxies, revealing modest turbulence levels that could offset cooling and informing future X-ray observations.

Contribution

It introduces a combined resonance scattering and line broadening method to constrain turbulence in galaxy halos, with improved accuracy over previous measurements.

Findings

Mean 1D turbulent velocity ~110 km/s

Non-thermal pressure contribution ~6%

Turbulent heating can offset radiative cooling in galaxy cores

Abstract

We present significantly improved measurements of turbulent velocities in the hot gaseous halos of nearby giant elliptical galaxies. Using deep XMM-Newton Reflection Grating Spectrometer (RGS ) observations and a combination of resonance scattering and direct line broadening methods, we obtain well bounded constraints for 13 galaxies. Assuming that the turbulence is isotropic, we obtain a best fit mean 1D turbulent velocity of ~110 km/s. This implies a typical 3D Mach number ~0.45 and a typical non-thermal pressure contribution of ~6 per cent in the cores of nearby massive galaxies. The intrinsic scatter around these values is modest - consistent with zero, albeit with large statistical uncertainty - hinting at a common and quasi-continuous mechanism sourcing the velocity structure in these objects. Using conservative estimates of the spatial scales associated with the observed turbulent motions, we find that turbulent heating can be sufficient to offset radiative cooling in the inner regions of these galaxies (<10 kpc, typically 2-3 kpc). The full potential of our analysis methods will be enabled by future X-ray microcalorimeter observations.

Figures

Tables

Table 1. Table 1 : Properties of the sample of elliptical galaxies studied in this work.

Source	Alternative	Chandra total	XMM-Newton	Distancea	Average temp.	Sound speed	$r_{eff}^b$	$r_{eff}$
	name	exposure [ks]	clean time [ks]	[Mpc]	[keV]	[km s-1]	[kpc]	referencec
IC 1459	-	60	156	21.1	0.70	430	3.5	B
NGC 507	-	44	95	65.5	1.19	560	1.7	D
NGC 533	A 189	40	35	137	0.93	500	14.5	M
NGC 708	A 262	140	173	69	1.32	590	11	S
NGC 1316	Fornax A	30	166	19	0.80	460	7.4	B
NGC 1332	-	60	64	19	0.80	460	9.2	R
NGC 1399	Fornax	130	124	19	1.00	520	32	Lo
NGC 1404	-	120	29	20	0.57	390	2.6	B
NGC 3411	NGC 3402	30	27	66.3	1.01	520	31	F
NGC 4261	-	100	135	29.4	0.68	450	5.7	T
NGC 4325	NGC 4368	30	22	108	0.86	480	14	L
NGC 4374	M 84	30	92	18.4	0.65	415	4.3	T
NGC 4406	M 86	30	64	16	0.81	460	7.9	B
NGC 4472	M 49	80	82	17.1	0.83	480	8.0	T
NGC 4552	M 89	200	29	15.3	0.58	390	2.3	T
NGC 4636	-	200	103	14.3	0.61	400	7.0	B
NGC 4649	M 60	310	130	17.3	0.87	480	6.5	T
NGC 4696	A 3526	760	153	44	1.14	550	82	Mi
NGC 4761	HCG 62	120	165	60	0.83	470	3.8	Sp
NGC 5044	-	70	127	38.9	0.82	480	10.4	T
NGC 5813	-	140	147	29.7	0.72	440	8.1	H
NGC 5846	-	170	195	26.3	0.63	410	9.8	H

Table 2. Table 2 : Properties of the Fe  XVII line transitions considered in this work, adopted from AtomDB database ver. 2.0.2.

wavelength	energy	lower	upper	oscillator	electron configuration		transition	Rayleigh scattering
$\left[\text{Å}\right]$	[keV]	level	level	strength	lower	upper	type	weight, $w_R$
15.01	0.826	1	27	2.49	2p6, 1S, J=0	2p5 3d, 1P, J=1	electric dipole	1
17.05	0.727	1	3	0.126	2p6, 1S, J=0	2p5 3s, 2P3/2, J=1	electric dipole	1
17.10	0.725	1	2	5.2$\cdot {10}^{-8}$	2p6, 1S, J=0	2p5 3s, 2P3/2, J=2	magnetic quadrupole	-

Table 3. Table 3 : Constraints on turbulence in our sample of elliptical galaxies, divided into subgroups according to the availability of the resonant scattering limit derived (Sect.  4.1 ), and method used. RS: resonant scattering-only probability distributions (Sect.  4.1 ); RS+LB: resonant scattering-plus-line broadening probability distributions (Sect.  4.2 ). Results are shown for: M 𝑀 M – 3D Mach number, v 1 ​ D subscript 𝑣 1 𝐷 v_{1D} – line-of-sight turbulent velocity amplitude, and ϵ t ​ u ​ r ​ b / ϵ t ​ h subscript italic-ϵ 𝑡 𝑢 𝑟 𝑏 subscript italic-ϵ 𝑡 ℎ \epsilon_{turb}/\epsilon_{th} – turbulent to thermal pressure fraction. The RGS measured flux ratio with 1 σ 𝜎 \sigma statistical uncertainty, along with the physical size of the RGS extraction region (the slit width; cf. Fig.  4 ) are also provided. Note that these measurements are performed using our fiducial model. We discuss in detail the effects of systematic uncertainties and model assumptions in Section  5 .

I. Bounded constraints
Source	RGS slit	Measured	RS-only 1$\sigma$/68% limits		RS+LB 1$\sigma$/68% limits
name	width	flux ratio	$M$	$v_{1D}$	$M$	$v_{1D}$	${ϵ}_{turb}/{ϵ}_{th}$
	[kpc]			[km  s-1]		[km  s-1]	[%]
NGC 4636	4.0	1.95 $\pm$ 0.09	${0.52}_{-0.22}^{+0.22}$	${121}_{-35}^{+51}$	${0.52}_{-0.15}^{+0.22}$	${121}_{-36}^{+51}$	${12}_{-7}^{+15}$
NGC 5813	7.4	1.8 $\pm$ 0.1	${0.44}_{-0.12}^{+0.21}$	${111}_{-31}^{+54}$	${0.37}_{-0.09}^{+0.12}$	${94}_{-24}^{+29}$	${6.3}_{-2.7}^{+5.9}$
II. Upper limits
Source	RGS slit	Measured	RS-only 1$\sigma$/68% limits		RS+LB 1$\sigma$/68% limits
name	width	flux ratio	$M$	$v_{1D}$	$M$	$v_{1D}$	${ϵ}_{turb}/{ϵ}_{th}$
	[kpc]			[km  s-1]		[km  s-1]	[%]
NGC 1316	4.4	1.8 $\pm$ 0.1	${0.23}_{-0.23}^{+0.24}$	${61}_{-61}^{+63}$
NGC 4374	3.2	2.1 $\pm$ 0.2	$0_{-0}^{+0.26}$	$0_{-0}^{+63}$	$0_{-0}^{+0.19}$	$0_{-0}^{+47}$
III. Lower limits
Source	RGS slit	Measured	RS-only 2$\sigma$/95% limits		RS+LB 1$\sigma$/68% limits
name		flux ratio	$M$	$v_{1D}$	$M$	$v_{1D}$	${ϵ}_{turb}/{ϵ}_{th}$
	[kpc]			[km  s-1]		[km  s-1]	[%]
NGC 1404	4.6	2.0 $\pm$ 0.2	$>$ 0.46	$>$ 103	${1.02}_{-0.39}^{+0.58}$	${230}_{-90}^{+130}$	${35}_{-18}^{+38}$
NGC 3411	15	1.1 $\pm$ 0.3	$>$ 0.15	$>$ 46	${0.58}_{-0.38}^{+0.66}$	${170}_{-110}^{+200}$
NGC 4261	1.1	1.9 $\pm$ 0.5	$>$ 0.079	$>$ 19	${0.29}_{-0.23}^{+0.43}$	${71}_{-57}^{+105}$
NGC 4325	25	1.4 $\pm$ 0.6	$>$ 0.12	$>$ 34	${0.86}_{-0.57}^{+0.83}$	${240}_{-160}^{+230}$
NGC 4552	3.6	1.6 $\pm$ 0.3	$>$ 0.22	$>$ 49	${0.79}_{-0.49}^{+1.31}$	${180}_{-110}^{+290}$	$8_{-8}^{+46}$
NGC 4649	4.0	1.3 $\pm$ 0.2	$>$ 0.081	$>$ 23	${0.26}_{-0.19}^{+0.32}$	${71}_{-51}^{+91}$
NGC 4761	14	1.3 $\pm$ 0.1	$>$ 0.23	$>$ 62	${0.61}_{-0.33}^{+0.41}$	${166}_{-90}^{+114}$
NGC 5044	9.6	1.3 $\pm$ 0.1	$>$ 0.30	$>$ 83	${0.61}_{-0.28}^{+0.39}$	${172}_{-79}^{+108}$	$8_{-6}^{+35}$
NGC 5846	7.4	1.7 $\pm$ 0.2	$>$ 0.24	$>$ 56	${0.32}_{-0.14}^{+0.25}$	${77}_{-34}^{+58}$	$3_{-3}^{+12}$
IV & V. No resonant scattering limit
Source	RGS slit	Measured	Reason behind
name	width [kpc]	flux ratio	the lack of limit
NGC 1332	4.4	2.7 $\pm$ 0.8	qualitative description
NGC 4406	3.8	2.1 $\pm$ 0.3	(see Sect. 4.1.IV);
NGC 4472	1.5	2.2 $\pm$ 0.3	additional data necessary
NGC 507	15	1.0 $\pm$ 0.4	low concentration
NGC 708	16	1.4 $\pm$ 0.2	of Fe XVII ions
IC 1459	5.0	1.7 $\pm$ 0.5	very large scatter
NGC 533	32	2.1 $\pm$ 0.7	on measured line ratios;
NGC 1399	4.4	1.3 $\pm$ 0.2	for further improvements
NGC 4696	10	1.5 $\pm$ 0.1	additional data necessary

Equations

$$Z_{peaked}(r)=0.65\times \frac{2.0+{\left(\frac{r}{0.5r_{eff}}\right)}^3}{1.0+{\left(\frac{r}{0.5r_{eff}}\right)}^3}-0.3[{\text{Z}}_{\text{sun}}].$$

$$\tau ={\int }_0^{\infty }{n}_i{\sigma }_{0}ds,$$

$${\sigma }_0=\sqrt{\pi }hc{r}_e\frac{f}{\Delta E_D}.$$

$$\Delta E_D=\frac{E_0}{c}{\left(\frac{2k{T}_e}{A{m}_p}+\frac{2}{3}{V}_{turb}^2\right)}^{0.5},$$

$$\text{FR}(r_p,M)=\frac{I_{17.05[\text{A˚}]}(r_p,M)+I_{17.10[\text{A˚}]}(r_p,M)}{I_{15.01[\text{A˚}]}(r_p,M)}.$$

$$\text{IFR}(M)=\frac{{\int }_{slab}(I_{17.05[\text{A˚}]}(r_p,M)+I_{17.10[\text{A˚}]}(r_p,M))dA}{{\int }_{slab}{I}_{15.01[\text{A˚}]}(r_p,M)dA}.$$

$$v_{1D}=\frac{1}{\sqrt{3}}M{c}_s=\frac{1}{\sqrt{3}}M\sqrt{\frac{\gamma k{T}_e}{\mu m_p}}.$$

$${ϵ}_{turb}=\frac{3}{2}\varrho v_{1D}^2=\frac{1}{2}\varrho c_s^2{M}^2,$$

$${ϵ}_{th}=\frac{3}{2}\frac{\varrho kT}{\mu m_p}.$$

$$\frac{{ϵ}_{turb}}{{ϵ}_{th}}=\frac{\gamma }{3}{M}^2.$$

$$M_l=0.13{\left(\frac{n_e}{10^{-2}{\text{cm}}^{-3}}\right)}^{1/3}{\left(\frac{c_s}{1000\text{ km s−1}}\right)}^{-1}{\left(\frac{l}{10\text{ kpc}}\right)}^{1/3}.$$

Full text

††pubyear: 2017††pagerange: Improved measurements of turbulence in the hot gaseous atmospheres of nearby giant elliptical galaxies–A

1 Introduction

Giant elliptical galaxies are filled with hot ($\sim 10^{7}$ K), X-ray emitting gas. Various physical processes, e.g. galaxy mergers, supernova explosions, and AGN activity, can perturb this gas and induce gas motions. These motions transport energy, mass, and metals, influencing the thermodynamic state of galaxies. Therefore, measurements of X-ray gas velocities are crucial for understanding galaxy formation and evolution (e.g. Sijacki et al., 2007; Weinberger et al., 2017), radio–mechanical AGN feedback (e.g. Brüggen et al., 2005; Scannapieco & Brüggen, 2008), and transport processes (e.g. Roediger et al., 2013; Kunz et al., 2014).

A direct way to probe gas velocity field is by measuring spectral line broadening (differential motions), and shifts in line centroids (bulk velocities). Recently, the Hitomi satellite measured a velocity broadening of 187$\pm$13 km s*-1* in the inner 30 kpc of Perseus cluster, where the galaxy NGC 1275 resides (Hitomi Collaboration et al., 2016). If these motions come from turbulence triggered by AGN-blown bubbles (on 20–30 kpc scales), then the associated heat dissipation would be sufficient to offset radiative cooling (Hitomi Collaboration et al., 2016). This result is consistent with the velocity structure inferred from the analysis of X-ray surface brightness fluctuations in the Perseus Cluster (Zhuravleva et al. 2014; see also results for the Virgo and Centaurus clusters by Zhuravleva et al. 2014 and Walker et al. 2015).

For most giant elliptical galaxies and clusters, however, detailed gas velocity information is lacking. Additional measurements, extending to more systems, are vital to better understand the role of turbulent heating, as well as other processes, such as e.g. weak shocks and sound waves (e.g. Fabian et al., 2006; Randall et al., 2015; Fabian et al., 2017), cosmic ray heating (e.g. Guo & Oh, 2008; Sijacki et al., 2008; Ruszkowski et al., 2017; Jacob & Pfrommer, 2017), bubble mixing (e.g. Hillel & Soker, 2016), radiative heating (e.g. Nulsen & Fabian, 2000), and turbulent mixing (e.g. Kim & Narayan, 2003).

The compact, cool, X-ray bright galaxies can be analyzed using high resolution X-ray spectra from Reflection Grating Spectrometer (RGS). Applying it to a sample of group central galaxies, Sanders & Fabian (2013) and Pinto et al. (2015) provided velocity upper limits of $\sim$ 300 km s*-1*. A major systematic uncertainty associated with the spatial extent of the source, which additionally broadens the spectral lines, typically limits these constraints to upper bounds only.

A promising indirect method of probing gas motions is resonant scattering effect. The X-ray emitting gas in elliptical galaxies is optically thin in the continuum and most line emission (i.e. the optical depth for free-free absorption is $\tau\sim 10^{-29}$, and is $\sim 10^{-2}$ for Thomson scattering). However, in the X-ray brightest resonance lines of abundant ions, the optical depth can be greater than one (Gilfanov et al., 1987). This causes photons to be absorbed and then quickly re-emitted, leading to line flux suppression in a galaxy or cluster core (e.g. Shigeyama, 1998). Small scale turbulent gas motions broaden the line, lowering its optical depth and reducing this effect. Thus resonant scattering can be used as a sensitive velocity diagnostic tool (for a review, see Churazov et al., 2010).

For galaxies with mean temperatures $\sim$0.3-1.0 keV, the Fe XVII 15.01 Å (optically thick), 17.05 Å and 17.1 Å (optically thin) lines are the most suitable for resonant scattering analyses, because their emissivity, along with the Fe XVII ionic fraction, peak in this temperature range (Fig. 1). By using the ratio of these lines, velocity amplitudes of the order of $\sim$100 km s*-1* have been measured in the cores of 3 elliptical galaxies (Xu et al., 2002; Werner et al., 2009; de Plaa et al., 2012), and Perseus cluster (Churazov et al., 2004; Gastaldello & Molendi, 2004).

In this work, we extend this resonant scattering analysis to a sample of 22 massive elliptical galaxies. We combine our resonant scattering measurements with independent line broadening results to obtain the best constraints to date on the turbulent velocity amplitudes, Mach numbers and non-thermal pressure contributions in giant elliptical galaxies, providing bounded constraints for 13 objects. This enables us, for the first time, to study common kinematic properties of the X-ray gas in elliptical galaxy cores.

The paper is organized as follows. We describe the RGS and Chandra data analysis in Section 2. The resonant scattering effect and simulations are described in Section 3. The results of the resonant scattering–only and resonant scattering–plus–line broadening analysis are presented in Section 4. Section 5 discusses the major assumptions and uncertainties in our study. We discuss our findings and their implications in Section 6 and provide conclusions in Section 7.

Throughout the paper the abundance of heavy elements is given relative to the proto-solar abundances by Anders & Grevesse (1989).

2 Observations and data analysis

2.1 Sample selection

The sources studied in this work constitute a subsample of the CHEmical Enrichment RGS cluster Sample (CHEERS) catalog of X-ray bright galaxy groups, clusters and elliptical galaxies. Specifically it includes galaxies with O VIII 19Å line detection (de Plaa & Mernier, 2016), plus two further cool galaxies with Fe XVII emission detected (NGC 1332 and IC 1459). From this initial group we selected 22 objects in which the Fe XVII lines are detected. The properties of the sample are summarized in Table 1. The XMM-Newton observations are listed in Table 1 in Pinto et al. (2015), with addition of $\sim$120 ks of new data for IC 1459, awarded during XMM-Newton AO-14.

2.2 RGS data analysis

The XMM-Newton satellite is equipped with two main X-ray instruments: the RGS and European Photon Imaging Camera (EPIC). We have used the RGS data for our main spectral analysis and the EPIC (a MOS detector) data for imaging. The RGS spectrometers are slitless and the spectral lines are broadened by the source extent. As in Pinto et al. (2015), we corrected for spatial broadening through the use of EPIC-MOS surface brightness profiles, but used newer calibration files for data reduction and software versions (available from June 2016). We used the XMM-Newton Science Analysis System (SAS) v15.0.0, and corrected for contamination from soft-proton flares using the standard procedure described in Pinto et al. (2015).

For most objects, we adopted a slit (spectral extraction region) width of $\sim$ 0.8’ ($\sim$ 5 kpc for most galaxies, cf. Table 3), providing good coverage of the inner Fe XVII bright core, and maximizing the equivalent widths of the Fe XVII lines with respect to those produced by the hotter gas phase (see e.g. Pinto et al. 2016). For a few objects (NGC 4261, NGC 4374, NGC 4472, and NGC 5044) we extracted RGS spectra from regions maximizing the detection of resonant scattering (Sect. 6.4).

We subtracted a model background spectrum, using the standard RGS pipeline and a template background file based on the count rate in CCD 9. We produced MOS 1 images in the $8-27$ Å wavelength band and extracted surface brightness profiles to model the RGS line spatial broadening with the relation: $\Delta\lambda=0.138\,\Delta\theta\,{\mbox{\AA}}$ (see the XMM-Newton Users Handbook).

2.2.1 Baseline model

Our analysis focused on the $8-27$ Å first and second order RGS spectra. We performed the spectral analysis with SPEX version 3.00.00, using C-statistics and adopting 68 per cent errors.

For a full discussion on the spectral modeling we refer the reader to Pinto et al. (2016). Briefly, we have described the ICM emission with a model for an isothermal plasma in collisional ionization equilibrium (cie; ionization balance is adopted from Bryans et al. 2009). The basis for this model is given by the Mekal code (Kaastra et al., 1996), but several updates have been included (see the SPEX manual). The free parameters in the fits were the emission measures $Y=n_{\rm e}\,n_{\rm H}\,dV$, temperature $T$, and the abundances of N, O, Ne, Mg, and Fe. The nickel abundance was fixed to that of iron. Most objects required two cie components to obtain an acceptable fit. In these cases we coupled the abundances of the two cie components because the spectra do not allow us to measure them separately. The cie emission models were corrected for redshift, Galactic absorption, and line-spatial-broadening through the multiplicative lpro component in SPEX, which uses as input the MOS 1 surface brightness profile (Sect. 2.2).

We did not explicitly model the cosmic X-ray background in the RGS spectra because any diffuse emission feature would be smeared out into a broad continuum-like component. For each source, we have simultaneously fitted the spectra of individual observations by adopting the same model. This gives a good description of the broadband spectrum, but, as previously shown in Pinto et al. (2015), underestimates the 17 Å Fe XVII line peaks for several sources due to unaccounted for resonant scattering, which we model separately (cf. following Section). In Fig. 2 we show an example of a spectrum of NGC 4636.

2.2.2 Fe XVII line measurements

We have measured the fluxes of the Fe XVII resonant and forbidden lines by removing all lines associated with the Fe XVII ion from our plasma model (due to unaccounted for resonant scattering, cf. previous Section), and fitting instead four delta lines broadened by the instrumental response fixed at 15.01 Å, 15.26 Å, 16.78 Å, and 17.08 Å, which are the main Fe XVII transitions dominating the band considered. The lines were also corrected for redshift, galactic absorption and spatial broadening following the cie components. This method has been successfully used in previous papers (e.g. Werner et al. 2009, de Plaa et al. 2012, Pinto et al. 2016). From those fits we calculated the ratio of the Fe XVII forbidden to resonant lines for all sources. The results are shown in Table 3.

In Pinto et al. (2016) we showed that the low-temperature O VII and Fe XVII lines have widths narrower than the hotter O VIII and Fe XVIII lines. Therefore, in our fits, we have used two different lpro components: one lpro for the (hotter) cie component and the other lpro for the cooler O VII and Fe XVII delta lines. The scale parameters s of the two lpro components were uncoupled and free parameters in the fits.

2.2.3 Line broadening analysis

To provide further constraints on turbulence, we used in our analysis probability distributions on measured line widths using the method described by Pinto et al. (2015). Starting from our baseline model of two thermal cie components (Sect. 2.2.2), and using the EPIC surface brightness profiles, which provide an approximate spatial mapping for the lines in our spectra, we performed spectral fits and evaluated the C-statistics on a fixed velocity grid, with other parameters left free to vary. In particular, the lpro spatial scale factor s=0–1 (i.e no spatial broadening and full EPIC broadening) was not fixed. This procedure is asymptotically equivalent to finding the marginalized velocity probability distribution.

2.3 Chandra data analysis

The initial data processing is done following the standard procedure described in Vikhlinin et al. (2005). The point sources are detected using the wvdecomp tool and excluded from the analysis. Correcting for the exposure, vignetting effects and subtracting the background, images of the galaxies are produced (Fig. 4).

The deprojected number electron density and temperature are obtained from projected spectra using the procedure described in Churazov et al. (2003). The deprojected spectra are fitted with an isothermal APEC plasma model (Smith et al., 2001; Foster et al., 2012) in the 0.6–8 keV band using XSPEC (ver. 12.8.0). The fitted model takes into account the total galactic HI column density and assumes fixed constant abundance of heavy elements 0.5 Z*☉*. Examples of the deprojected profiles are shown in Fig. 4.

For several galaxies in our sample (NGC 708, NGC 1404, NGC 1399, NGC 4261, NGC 4406, and NGC 4472) we used published deprojected radial profiles from Werner et al. (2012). The deprojected data for NGC 4696 were provided by Sanders et al. (2016).

3 Simulations

For all objects in our sample, we conducted radiative transfer Monte Carlo simulations of the resonant scattering (Sect. 3.3). These simulations predict the fluxes of the 15.01, 17.05 and 17.1 Å Fe XVII lines, assuming different Mach numbers of turbulence, which are then compared to the measured flux ratios. We illustrate the analysis steps below using NGC 5813 and NGC 4636. Details for the rest of the objects are presented in Appendix A.

3.1 Input models

For our resonant scattering simulations we adopted a spherically symmetric model of each galaxy based on the interpolated deprojected profiles of the gas electron number density and temperature (orange lines in Fig. 4; Sect. 2.3). In order to account for the uncertainty associated with 1$\sigma$ errors in the deprojected data, we vary the models within plotted 68 per cent errors and repeat the calculations.

Since the abundance measurements of the heavy elements are uncertain, we performed simulations conservatively assuming a flat abundance profile fixed at 0.5 Z*☉*. The sensitivity of our results to the choice of the abundance model was checked by additionally considering a centrally peaked abundance profile, scaled by the galaxy’s optical effective (half-light) radius $r_{eff}$, namely:

[TABLE]

In this case, the abundance is 1 Z*☉* in the galaxy center and drops to 0.35 Z*☉* in the outskirts. Both models are shown in the bottom panels of Fig. 4. Effective radii used are listed in Table 1. As we discuss later, for most galaxies the choice of abundance model does not affect the results (Sect. 5.2).

3.2 Optical depth in the Fe XVII line

The optical depth $\tau$ of a galaxy in a given line is:

[TABLE]

where $s$ is the distance along the photon propagation, $n_{i}$ is the number density of the ion in the ground state and $\sigma_{0}$ is the scattering cross section at the center of the line, given by:

[TABLE]

Here $h$ is Planck’s constant, $r_{e}$ is the classical electron radius, $c$ is the speed of light, $f$ is the oscillator strength of the respective atomic transition, and $\Delta E_{D}$ is the Doppler line width. $\Delta E_{D}$ is given by:

[TABLE]

where $E_{0}$ is the rest frame energy of the atomic transition, $k$ is the Boltzmann constant, $A$ is the atomic mass number, $m_{p}$ is the proton mass, $T_{e}$ is the electron temperature, and $V_{turb}$ is the characteristic 3D turbulent velocity. We parametrize turbulence by the 3D Mach number111In this work we assume isotropic turbulence, i.e. $V_{turb}=\sqrt{3}v_{1D}$, where $v_{1D}$ is the 1D differential velocity component. Our simulations assume fixed Mach number everywhere in the galaxy. Running simulations for fixed turbulent velocity instead changes our results by a maximum of 5  km s*-1* in only one galaxy., $M=V_{turb}/c_{s}$, where $c_{s}=\sqrt{\gamma kT/(\mu m_{p})}$ is the sound speed ($\gamma=5/3$ is the adiabatic index for an ideal monoatomic gas, and $\mu=0.6$ is the mean particle atomic weight).

Assuming no differential gas motions, the optical depths in the 15.01 Å line calculated for all galaxies in our sample are shown in Fig. 5. Most of the objects are optically thick in this line, and for almost a half of the sample $\tau$>2. NGC 1404 has a very large optical depth of $\sim$9–10, due to the combination of its large density and low temperature, resulting in a high ionic Fe XVII fraction. The other two lines considered in this study, 17.05 Å and 17.10 Å, are optically thin because of their low oscillator strengths (cf. Table 2).

3.3 Resonant scattering modeling

Our Monte Carlo simulations of resonant scattering follow the simulations performed by Sazonov et al. (2002), Churazov et al. (2004), and Zhuravleva et al. (2010, 2011). Namely, we randomly draw the position and propagation direction of each photon (total number of photons >$10^{7}$), and draw its energy from a Doppler-broadened Gaussian around the line energy. Initially we assign a unit weight to the photon, which is then reduced after each scattering event by a factor of 1-$e^{-\tau}$, until a minimal threshold ($\sim$10*-9*) is reached. Photons can undergo multiple scatterings before they leave the galaxy. After each event a new position and propagation direction are drawn using a phase function, that is a sum of the isotropic and Rayleigh (dipole) scattering phase functions with appropriate weights (Hamilton, 1947). We use ionization balance data and line emissivities from the APEC model for optically thin plasmas (Smith et al., 2001; Foster et al., 2012, AtomDB ver. 2.0.2222http://www.atomdb.org/). Line transition properties and dipole scattering weights are listed in Table 2.

3.4 Calculating the Fe XVII line flux ratio

Our Monte Carlo simulations provide projected line fluxes $I_{M}$ as a function of projected radius $r_{p}$, given a specific 3D Mach number $M$. These profiles take into account resonant scattering, along with thermal and turbulent line broadening. The primary quantity of interest is the projected flux ratio (FR) of optically thin (17.05 Å, 17.10 Å) to thick (15.01 Å) Fe XVII lines (the 17.05 Å and 17.10 Å lines are observationally indistinguishable, thus their sum is considered). For each object in our sample, we predicted the projected radial profiles of FR varying levels of turbulence (parametrized by the Mach number $M$):

[TABLE]

An example is shown in Fig. 7.

The observed flux ratio comes from a spatially extended RGS spectral extraction region (shown in Fig. 4). We numerically integrate line fluxes over this region $A$ (a 0.8*′* wide slab333For some objects (NGC 4261, NGC 4374, NGC 4472, and NGC 5044) we actually use narrower slits to maximize the resonant scattering signal (Sect. 6.4).):

[TABLE]

This integrated flux ratios (IFRs) are then compared to observations, as illustrated in Fig. 7.

4 Results

We present two sets of results: first, based on resonant scattering effect only; and second, using combined resonant scattering and line broadening methods. In the main text we present detailed results for NGC 4636 and NGC 5813. The rest of the sample is shown in Fig. 16 in Appendix A444We show all galaxies for which the effect of resonant scattering is important.. Results are summarized in Table 3.

4.1 Resonant scattering–only

We first compare our observations (red line and region in Fig. 7) to our fiducial model for the integrated flux ratio, namely simulations run for a flat abundance profile and deprojected thermodynamic profiles without uncertainties (blue line in Fig. 7). This follows the approach of previous resonant scattering works, e.g. Werner et al. (2009) and de Plaa et al. (2012). Lower limits for 8 galaxies can be derived this way555M89, NGC 1404, NGC 4261, NGC 4325, NGC 4636, NGC 4649, NGC 5813 , and NGC 5846., on average showing $M>0.59$ ($v_{1D}>133$ km s*-1*). NGC 4261 has the lowest lower limit on Mach number, $M>0.054$ ($v_{1D}>13$ km s*-1*), while NGC 1404 shows the largest lower limit, $M>0.59$ ($v_{1D}>130$ km s*-1*). For the remainder of the sample we cannot obtain any limits using this approach.

In order to extract our formal constraints on the Mach number, we approximated the uncertainties on the predicted IFR (blue regions in Fig. 7) as Gaussians. We then convolved this uncertainty with the statistical error on the observed ratio, and calculated the probability density function (pdf) of a Mach number. The normalized pdfs are shown with black curves in Figs. 7, 16. The peaks of the pdfs are indicated with the vertical dashed lines, where appropriate (in 7 galaxies). Note that in most cases the peaks coincide with the intersection of the blue (simulated ratio for fiducial model) and the red (measured ratio) curves.

Assuming that the turbulence in galaxies is subsonic, i.e. $M<1$, confidence intervals are obtained from the pdfs. Green regions in Fig. 7 show the 68 per cent confidence intervals, providing constraints of $M=0.44^{+0.21}_{-0.12}$ ($v_{1D}=111^{+54}_{-31}$ km s*-1*) in NGC 5813 and $M=0.52^{+0.22}_{-0.15}$ ($v_{1D}=121^{+51}_{-35}$ km s*-1*) in NGC 4636. We obtain well bounded constraints, and upper or lower limits for 11 other systems: NGC 1316, NGC 1404, NGC 3411, NGC 4261, NGC 4325, NGC 4374, NGC 4552, NGC 4649, NGC 4761, NGC 5044, and NGC 5846. For 3 galaxies, the pdfs show a preference for lower Mach numbers, but are too flat to derive meaningful upper limits; for 6 galaxies the distributions are completely flat, thus we cannot constrain turbulent velocities in these objects with resonant scattering. For several of these galaxies it would be straightforward to obtain better resonant scattering measurements provided more data (Sect. 6.4).

Below we summarize the derived constraints, listed in Table 3, by dividing galaxies into 5 groups. Summary plot for groups I—III is shown in Fig. 8 (left), with group I shown in blue, group II in purple, and group III in black. The sensitivity of the results to the assumed maximum Mach number $M_{max}=1$ (the prior) is discussed in Sect. 5.5.

I. Peaked distributions: bounded constraints. Two galaxies, NGC 4636 and NGC 5813, show clearly peaked distributions that allow us to report the most probable value with 68 per cent confidence (lower and upper limit; Fig. 7). Changing the Mach number prior does not affect the results significantly.

II. Peaked distributions: low turbulence. Two more objects have clearly peaked distributions: NGC 4374 and NGC 1316 (Fig. 16). Both galaxies have low turbulence, and the confidence intervals do not provide meaningful lower limits. However, since the only difference between the former and latter groups is that the distributions are shifted towards smaller Mach numbers, we treat them the same way as galaxies in group I and report the most probable value with a 68 per cent upper limit and a lower limit of 0.

III. Lower limits. Resonant scattering technique is better suited for providing lower rather than upper limits on gas motions velocities: the stronger the turbulence, the smaller the line suppression (Sect. 3.2). Therefore the integrated flux ratio in the case of large Mach numbers approaches the constant optically thin plasma case (cf. the blue and yellow lines in Fig. 7). Since pdfs flatten at large $M$ (cf. Fig. 16), our velocity constraints depend on maximum Mach number $M_{max}$ assumed. We note that lower limits are least sensitive to the choice of Mach number prior (Sect. 5.5).

For the majority of the objects in our sample (9; see Table 3) we are able to provide lower limits only (at 95 per cent confidence; for pdfs see Fig. 16). Among these objects, three galaxies also show the most probable value (NGC 1404, NGC 4261, and NGC 5846). The mean lower limit is 0.178 (47 km s*-1*), excluding NGC 1404, which is an obvious outlier (lower limits: $M>0.46$, $v_{1D}>103$ km s*-1*).

IV. Low turbulence - qualitative description. Three galaxies, NGC 1332, NGC 4406, and NGC 4472, have high observed flux ratios, indicating that the optically thick line is suppressed due to resonant scattering. This points towards low turbulence, which is reflected in the pdfs of these objects (Fig. 16). The effect itself is not strong, and the resulting probability distributions are too flat for deriving limits. However, we can see that the pdf at $M=0$ is approximately $\sim$5 times more than at $M=0.5$ or $M=1$ in NGC 4406, $\sim 3$ times more likely in NGC 4472 and $\sim$2 times more likely in NGC 1332.

V. No limits. For 6 galaxies we are not able to derive any turbulence constraints. NGC 708 and NGC 507 have the largest gas temperatures in our sample and the resonant Fe XVII line is optically thin. Other objects (e.g. NGC 1399, NGC 4696) are more distant, thus their innermost regions, where most of the scattering occurs, have angular sizes significantly smaller than the RGS aperture used. Current RGS data does not allow us to measure line ratios reliably in such regions (Sect. 6.4).

The characteristic line-of-sight one-component turbulent velocity amplitude $v_{1D}$ can be derived directly from the 3D Mach number. If turbulence is isotropic, then:

[TABLE]

The temperature $T_{e}$ that we use here is the mass weighted average electron temperature calculated within the spectral extraction region from the deprojected temperature profile. The temperatures of galaxies, along with respective sound speeds, are shown in Fig. 9 and Table 1. The derived turbulent velocity constraints are listed in Table 3, and shown in the right panel of Fig. 8. Typical lower limits are 20–60 km s*-1*. For a few objects the measured velocities are between 43–121 km s*-1*.

4.2 Resonant scattering–plus–line broadening

The velocity dispersion of the X-ray emitting gas can be measured directly through line broadening. Since the RGS is a slitless spectrometer, the spatial extent of the galaxy core broadens the lines in addition to natural, thermal and turbulent broadening. Therefore, direct velocity measurements provide mostly upper limits (e.g. Pinto et al., 2015, and Sect. 2.2). We obtained the line broadening velocity probability distributions by performing spectral fitting, varying the velocity and evaluating the C-statistics each time (Sect. 2.2.3). These pdfs are then combined by multiplying with the pdfs from the resonant scattering analysis (Sect. 4.1).

Fig. 10 illustrates the result of this procedure for NGC 5846. The blue line shows the resonant scattering pdf, which provides only a lower limit on the velocity, while the red line shows the line broadening pdf, which gives only an upper limit. The combined distribution, shown in black, is peaked and narrow, and provides a velocity measurement with 68 per cent uncertainties (green region). Analogous plots for the remaining galaxies can be found in Fig. 11.

4.3 Exploring the sample properties

Using the combined distributions we are able to measure velocities of gas motions in 13 galaxies in our sample. We have examined the distribution of measured velocity values, which, in principle, can provide key information on e.g. processes that are responsible for the motions. A summary plot is shown in Fig. 12 (see also Table 3).

We fit the measured velocities and Mach numbers with single mean values, allowing for scatter, using Monte Carlo Markov Chain method. The resulting most probable values are $v_{1D,mp}=107^{+19}_{-15}$ km s*-1* and $M_{mp}=0.44^{+0.07}_{-0.06}$ (shown with red lines and regions in Fig. 12). In the case of both the velocity and Mach number, the scatter is consistent with zero with 1$\sigma$ upper limits of 38 km s*-1* and 0.16, respectively.

Note that by utilizing the line broadening pdfs, which provide upper limits, we derive these measurements with no prior maximum Mach number assumption, as opposed to the pure resonant scattering case (cf. Sect. 4.1).

4.4 Turbulent pressure

Knowing the characteristic Mach number, we can place constraints on the non–thermal pressure contributed by turbulence. The energy density of turbulence $\epsilon_{turb}$ is given by:

[TABLE]

where $\varrho$ is the gas mass density. On the other hand, the thermal energy density is:

[TABLE]

The fraction of the turbulent non–thermal to thermal pressure is a ratio of the two energy densities:

[TABLE]

In order to measure the turbulent pressure support we used the combined resonant scattering and line broadening probability distributions of Mach numbers (Sect. 4.2), and calculated respective pressure distributions. In Fig. 13 we show the resulting 68 per cent constraints on pressure support (listed in Table 3). The data are consistent with no scatter around a single constant value of 5.6${}_{-1.5}^{+2.6}$ per cent, shown with a red line in Fig. 13. The 1$\sigma$ upper limit on scatter is 2.6 per cent.

5 Systematic uncertainties

Our resonant scattering analysis makes a number of simplifying assumptions. Firstly, we assumed spherically symmetric models of galaxies, which is a crude approximation given that the morphology of some objects is quite disturbed (e.g. filamentary structure, bubbles etc.; see Sect. 6.4 for possible future improvements). Secondly, we fitted the deprojected spectra at a given radii with a single temperature model. This might introduce a bias, since the Fe XVII line emissivity and ionic fraction are strong functions of temperature (Fig. 1). For some galaxies there is no evidence that a multi-phase gas exists in a volume-filling way in their cores (e.g. in NGC 5044 and NGC 5813, de Plaa et al., 2012), while for others it is likely the case (e.g. in NGC 4696, Sanders et al., 2016). Finally, we have only considered isotropic turbulent motions, characterized by a single Mach number. If instead motions are anisotropic, the amplitude of line suppression due to scattering will change. Namely, if motions are predominantly in the radial direction, then for a given velocity amplitude the line suppression will be smaller than in the case of isotropic motions (Zhuravleva et al., 2011). Measuring anisotropy effects will require spatial mapping with future microcalorimeter-like high spectral resolution data (Sect. 6.5).

Other key major systematic uncertainties are associated with the line spread function of RGS, the abundance of heavy elements, current atomic data, charge exchange, and the choice of the maximal Mach number. We explore each of these in turn.

5.1 RGS instrumental uncertainty

The Line Spread Function of the RGS is known with accuracy of 5–10 per cent, making the instrument less sensitive to low velocity line broadening. This uncertainty has a small effect on the measured line flux ratios. Therefore it does not affect the majority of our results, since most pdfs at low velocities are dominated by the resonant scattering measurement, which relies on the observed line flux ratios.

There are two exceptions: NGC 1316 and NGC 4374, where the line broadening pdf is important at low velocities. However, in these two galaxies the resonant scattering and line broadening independently provide similar constraints. If line broadening was not included, the upper limits on velocities would rise by $\sim$50  km s*-1* in NGC 1316 and $\sim$15  km s*-1* in NGC 4374 (cf. Table 3). Larger uncertainties in these galaxies would reduce the limit on the scatter around the common sample velocity, leaving the best fit sample velocity unchanged. Therefore this effect does not affect our conclusions.

5.2 Abundance of heavy elements

Obtaining robust abundance measurements for elliptical galaxies from current X-ray spectra is challenging. Thus, we conservatively choose to use a flat abundance, fixed at 0.5 Z*☉*, as our default model. This value is consistent with recent average iron abundance profile for group central galaxies in the CHEERS sample (Mernier et al. 2017, in prep.).

In order to test sensitivity of our measurements to this assumption, we repeated the calculations assuming a peaked abundance model (Eq. 1, Sect. 3.1, and Fig. 4). For most galaxies the results only weakly depend on the adopted profile, with the difference $<20$ per cent. We illustrate this in NGC 5846 (Fig. 14, left panel), in which the lower limit on Mach number is increased by 18 per cent (10  km s*-1*), and the most probable value by 23 per cent (29  km s*-1*) if the peaked abundance model is assumed instead of the constant value of 0.5 Z*☉*. This is smaller than a nominal 68 per cent uncertainty almost by a factor of 2.

A few objects show substantial differences, $\sim$20–50 per cent (40–50  km s*-1*; NGC 1404, NGC 4261, NGC 4552, and NGC 4636). In these galaxies the physical size of the spectral extraction region is small compared to the half-light radius used to scale the peaked abundance profile, meaning that effectively the profile is flat within the extraction region with a value double the one adopted in the default flat model. This doubles the amount of Fe XVII ions present in the gas, leading to larger optical depths in considered lines (e.g. $\tau$ changing from $\sim 6$ to $\sim$ 12 in NGC 4636), which results in more efficient resonant scattering and slightly different constraints than in the default case.

We note that abundance profiles with a central drop are sometimes observed in elliptical galaxies (e.g. Panagoulia et al., 2015). However, this drop might be a result of fitting a simplified model to a multiphase gas in the galactic core (e.g. Buote et al., 2003). Therefore, we do not consider a model with a central drop in this work.

5.3 Atomic data

The Fe XVII ion used in our analysis provides critical spectral diagnostics. However, due to the complicated inner structure of the ion, complete agreement between experimental results and theoretical predictions of the atomic properties has not yet been reached (but is expected to be achieved when high order effects are included in calculations, e.g. Brown et al., 2006).

The two major current astrophysical plasma codes, APEC and SPEX, predict slightly different optically thin ratios of the lines considered in this work, e.g. for a 0.6 keV plasma, the ratio $\sim$1.5 is predicted by APEC and $\sim$1.3 by SPEX. Here we use APEC ver. 2.0.2 for our fiducial models666Using the latest AtomDB ver. 3.0.7 changes results by $\sim$1 per cent., because the respective atomic properties of Fe XVII are closer to the experimental measurements from EBIT and LCLS (Brown et al., 2001; Bernitt et al., 2012).

Future experiments providing smaller uncertainties on measured atomic properties, accompanied by precise calculations, are needed to match the precision of X-ray microcalorimeter-type missions, in order to fully enable the range of spectral diagnostics of the Fe XVII ion.

5.4 Charge exchange

Charge exchange between ions and neutral atoms or molecules could potentially mimic the effect of resonant scattering, since it enhances the forbidden line with respect to the resonant line. However, the magnitude of the effect is expected to be small in comparison with current uncertainties. Pinto et al. (2016) applied a simple charge exchange model to the elliptical galaxy NGC 4636, concluding that it did not affect the Fe XVII spectral lines, but only lines of ions tied to colder gas, e.g. O VII. Therefore we do not include this process in our current models.

5.5 Maximal Mach number

Deriving uncertainties on measured Mach numbers using resonant scattering probability distributions requires us to adopt a prior on the 3D Mach number range (Sect. 4.1). Motivated by numerical simulations and measured upper limits, we choose to consider only subsonic turbulence, $M_{max}=1$. In some cases, gas motions can be sufficiently strong to suppress the resonant scattering effect, i.e. the line ratio becomes consistent with the optically thin case. In such situations, the pdfs will be flat at large Mach numbers, and our constraints will therefore depend on the assumed maximal Mach number.

This is illustrated in the right side of Fig. 14, where the upper panel shows 68 per cent constraints in a peaked pdf in NGC 5813, and the lower panel shows 95 per cent lower limits in a non-peaked pdf in NGC 5044, for two different maximal Mach numbers: $M_{max}=1$ (our default) and $M_{max}=2$ (red and grey regions respectively). The lower limit in NGC 5813 is least affected by this assumption: the difference between the default case and larger $M_{max}$ is only 5 per cent (4  km s*-1*), while the upper limit increases by 9 per cent (12  km s*-1*). Uncertainties in other galaxies with peaked distributions behave similarly. In NGC 5044 the 2$\sigma$ lower limit increases by 50 per cent (34  km s*-1*), which is the case for most galaxies with flatter pdfs. Objects least affected are the ones with very peaked distributions, such as NGC 1404 (22 per cent/18  km s*-1* change) and NGC 5846 (27 per cent/12  km s*-1* change).

Note that the combined resonant scattering and line broadening pdfs (results in Figs.  12 and 13) are not affected by this assumption (Sect. 4.2).

6 Discussion

6.1 Comparison with previous measurements

Resonant scattering in three galaxies (NGC 4636, NGC 5044, and NGC 5813) has been previously examined using a similar approach, and the same data and codes, by Werner et al. (2009) and de Plaa et al. (2012). The main difference with respect to these works is in comparison of simulations and observations, and in combining of resonant scattering and line broadening constraints. Despite these differences, the results on resonant scattering are consistent with the previous works.

Our measurements also agree with estimations of shock-driven turbulent velocities in NGC 5813 (Randall et al., 2015), as well as with previous upper limits measured via line broadening with RGS data (Sanders et al., 2011; Sanders & Fabian, 2013; Pinto et al., 2015).

Interestingly, the cold interstellar medium (ISM) velocity dispersions mapped with C II in the cores of NGC 4636, NGC 5044, NGC 5813, and NGC 5846, match the hot gas velocity dispersions measured in this work, supporting the argument that the cold ISM cools out of the hot gas (Werner et al., 2014).

A recent Hitomi measurement in the inner 30 kpc region of the Perseus Cluster core (NGC 1275) showed velocity broadening of 187$\pm$13 km s*-1* and a non-thermal pressure contribution of $\sim$4 per cent (8 per cent accounting for sheer motions; Hitomi Collaboration et al., 2016). This velocity is close to the best fit sample values of 107${}_{-15}^{+19}$  km s*-1*, and 5.6${}_{-1.5}^{+2.6}$ per cent non-thermal pressure support measured in this work. The sample–averaged velocity is slightly lower than the one in Perseus, but also the regions we probe in this work are smaller (few kpc vs. few 10s kpc).

Our inferred non-thermal pressure contribution is consistent with observations of the cores of other giant ellipticals (NGC 1399 and NGC 4486, Churazov et al., 2008). Its low value encourages the use of hydrostatic equilibrium approximation for galaxy mass measurements with X-rays.

6.2 Comparison with numerical simulations

Detailed hydrodynamical simulations of AGN feedback by Gaspari et al. (2012) reproduce a level of subsonic turbulence consistent with our measurements. Within the inner few kpc, the time-averaged velocity dispersion varies from $\sim$60–200  km s*-1* in simulations, while our typical averaged results provide velocity $\sim$93–126  km s*-1*. Similarly, Valentini & Brighenti (2015) find hot gas velocity dispersions of 100–200  km s*-1* in the cores of simulated massive elliptical galaxies. A somewhat different conclusion was recently reached by Yang & Reynolds (2016), where the kinetic energy in AGN feedback simulations is only $\sim$1 per cent of the gas thermal energy (we find this fraction to be 5.6${}_{-1.5}^{+2.6}$ per cent).

The missing element in these simulations of AGN feedback is the effect of cosmological merging, which triggers additional gas motions (as shown in galaxy cluster cosmological simulations by e.g. Lau et al., 2009; Vazza et al., 2011).

6.3 Radiative cooling and turbulent heating balance

The inferred gas velocity values measured in all objects in our sample are comparable, and there is no detectable scatter around the best fit mean value (albeit with large statistical uncertainty). This may hint at a common origin of the velocity field, which could be sourced by a quasi–continuous feedback mechanism, with the most obvious candidate energy source being AGN, although additional contributions from e.g. merging activity may also be present (e.g. Ascasibar & Markevitch, 2006; ZuHone et al., 2010).

If indeed turbulence is produced by a feedback activity, it is interesting to estimate whether the turbulent energy dissipation is sufficient to balance the radiative cooling. By adopting an average value of the normalized cooling function $\Lambda_{n}\approx 1.5\cdot 10^{-23}$, which is representative for the temperatures and metallicities of considered galaxies, we can estimate the Mach number of turbulence $M_{l}$, associated with spatial scales of motions $l$, which provides the balance (Zhuravleva et al., 2014):

[TABLE]

A typical galaxy core electron number density in our sample is 0.05 cm*-3*, and sound speed is 450  km s*-1*. Both the typical size of the RGS extraction region and the effective length along the line of sight (distance that contributes 50 per cent of the flux at a given projected radius, see Zhuravleva et al., 2012), are about $\sim$ 5 kpc. If our measured velocities are dominated by gas motions on such scale, then $M_{l}\sim$0.4 should provide the cooling–heating balance. If, instead, scale associated with the measured velocity is smaller (larger), e.g. 1 kpc (10 kpc), then $M_{l}\sim$0.2 (0.5). Our measurements give an averaged $M\sim$0.44, meaning that the turbulence should typically be enough to offset the radiative cooling in the cores of massive elliptical galaxies.

Interestingly, we measured (or have strong hints of) weak turbulence in the most relaxed giant elliptical galaxies, NGC 4261, NGC 4472, and NGC 4649 (as identified by e.g. Werner et al., 2012), while galaxy with the largest measured velocity, NGC 1404, is very dynamically active, moving within and interacting with the ICM of the Fornax cluster (e.g. Machacek et al., 2005; Su et al., 2017). We also found a few potential exceptions in our sample, where we see the indications of an insufficient level of turbulence to balance cooling in the inner few kpc region. However, any firm conclusions require additional RGS data.

6.4 Further improvements

The statistical uncertainty on our measurements comes from the convolved errors from the RGS line flux measurements and the deprojected thermodynamic profiles from Chandra data. In most galaxies the RGS error is the dominant one and could be reduced by acquiring additional XMM-Newton data. The exceptions are NGC 1316 and NGC 4636, which require deeper Chandra observations.

The resonant scattering signal is stronger if considered in even smaller regions, where the optical depth is the largest. However, using smaller regions leads to lower photon counts and larger statistical uncertainties. Therefore, this approach also requires additional data for most objects, except for NGC 4261, NGC 4374, NGC 4472, and NGC 5044, where current data are sufficient to maximize the scattering signal.

Ahoranta et al. (2016) studied spatial the variation of the optically thin to thick line ratio in NGC 4636, suggesting high turbulence in the southern, and low in the northern region of the galaxy. In order to perform quantitative analysis of this asymmetry, it is necessary to perform Monte Carlo simulations similar to these discussed in this paper. However, such analysis requires more complex models of the galaxy geometry, relaxing the spherical symmetry assumption, which are beyond the scope of this paper.

6.5 Future microcalorimeter-type missions

Future X-ray missions with microcalorimeter-type detectors, such as e.g. Athena777http://www.the-athena-x-ray-observatory.eu/, Lynx888https://wwwastro.msfc.nasa.gov/lynx/, and Hitomi Recovery Mission, should deliver large volumes of spatially resolved data with superb spectral resolution. As shown by the Hitomi observation of the Perseus Cluster (Hitomi Collaboration et al., 2016), this will allow for direct measurements of gas bulk and turbulent velocities in the centers of clusters, directly from line widths and Doppler shifts, and indirectly through resonant scattering. For cooler objects, such as galaxies, with average temperature $\sim$1 keV, it might still be challenging to measure velocities through line broadening with $\sim$2.5-5 eV resolution microcalorimeters. Typical velocity found in this work (107  km s*-1*) causes the Fe XVII lines broadening of $\sim$0.5 eV, while even sonic motions would cause a sub-eV broadening in a cool, 0.75 keV gas. However, the microcalorimeter data will not suffer from the major systematic of current best instrument (RGS; the spatial line broadening), allowing for better resonant scattering and line broadening studies.

We show simulated Hitomi (left) and Athena (right) spectra of NGC 4636 in Fig. 15 for no turbulence (upper panels), and substantial turbulence ($M=0.45$, as measured in this work; lower panels). Resonant scattering causes suppression in the line center of $\sim$ 45 per cent for $M=0$ and $\sim$ 25 per cent for $M=0.45$, which can be clearly seen with just a 100 ks Hitomi or a 10 ks Athena observation.

7 Conclusions

In this work we have performed a detailed analysis of the resonant scattering effect in nearby, giant elliptical galaxies, thereby constraining the turbulent velocities of the hot gas in their cores. By combining the velocity constraints from resonant scattering with upper limits from spectral line broadening, we obtain significantly improved constraints on gas velocities, Mach numbers, and non-thermal pressure support. Our analysis combines high-resolution XMM-Newton RGS spectra, Chandra imaging and numerical simulations of the resonant scattering effect in these galaxies. Our main findings are as follows:

• •

Using the resonant scattering effect only, we measure 1D turbulent velocities in the cores of 4 massive elliptical galaxies ranging between 0–120  km s*-1* (3D Mach numbers 0–0.5), and place lower limits of 20–100  km s*-1* (3D Mach numbers 0–0.5) in a further 9 systems.

• •

By combining line broadening and resonant scattering measurements, we obtain interesting velocity constraints for 13 galaxies. The sample best fit values are: 1D velocity dispersion $\sim 110$  km s*-1*, 3D Mach number $\sim 0.45$, and non-thermal to thermal pressure fraction $\sim 6$ per cent. The scatter around these values is rather small, consistent with zero within uncertainties.

• •

Consistency with a single velocity supports a common gas heating mechanism in massive elliptical galaxies.

• •

For the majority of objects the measured turbulence is enough to balance the radiative cooling, assuming conservative estimates of spatial scales associated with the measured motions.

• •

The inferred non-thermal pressure contribution in the cores of giant galaxies is encouraging for hydrostatic mass measurements.

• •

In the near term, our analysis could be improved by acquiring additional XMM-Newton and Chandra data, and by advancing the models.

• •

In the long term, this approach can be used to interpret future high-resolution observations with Hitomi Recovery Mission, Athena, and Lynx. We highlighted the major sources of systematic uncertainties, e.g. abundance measurements and atomic data, which have to be addressed to enable full exploitation of the microcalorimeter data.

Acknowledgements

This work is based on observations obtained with XMM-Newton, an ESA science mission funded by ESA Member States and USA (NASA). CP acknowledges support from ERC Advanced Grant Feedback 340442 and new data from the awarded XMM-Newton proposal ID 0760870101. AO thanks J. Sanders for providing deprojected data for NGC 4696.

Appendix A Resonant scattering results for the remainder of the sample

In Fig. 16 we present resonant scattering–only results for the remaining galaxies, which have not been shown in the main text. For details, see Sects. 4.1.