Hidden cooling flows − IV. More details on Centaurus and the efficiency of AGN feedback in clusters

ABSTRACT

Cooling flows are common in galaxy clusters which have cool cores. The soft X-ray emission below 1 keV from the flows is mostly absorbed by cold dusty gas within the central cooling sites. Further evidence for this process is presented here through a more detailed analysis of the nearby Centaurus cluster and some additional clusters. Predictions of JWST near and mid-infrared spectra from cooling gas are presented. [Ne vi] emission at |$7.65\,\mu$|m should be an important diagnostic of gas cooling between 6 and |$1.5\times 10^5{\rm \, K}$|⁠. The emerging overall picture of hidden cooling flows is explored. The efficiency of active galactic nucleus feedback in reducing the total cooling rate in cool cores is shown to be above 50 per cent for many clusters but is rarely above 90 per cent. The reduction is mostly in outer gas. Cooling dominates in elliptical galaxies and galaxy groups that have mass flow rates below about |$15{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| and in some massive clusters where rates can exceed |$1000{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }.$|

1 INTRODUCTION

We have found that cooling flows are operating in most early-type galaxies (HCFI, II, III; Fabian et al. 2022, 2023a, b). The rapidly cooling, soft X-ray part of these flows is mostly hidden from direct view by photoelectric absorption in surrounding cold gas, much of which may be the product of the cooling process. Such hidden cooling flows (HCFs) have mass cooling rates of |$1\!-\!5{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| in typical elliptical galaxies rising to |$10\!-\!20{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| in brightest group galaxies (BGGs) to |$20\!-\!100{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| in brightest cluster galaxies (BCGs). Some exceptional distant clusters have higher rates of |$\dot{M}\sim 1000{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| or more.

The realization that X-ray absorbing gas must be present in cool core clusters began in 1991 (White et al. 1991) and its development thereafter is discussed in HCFI. It was initially added outside the soft X-ray emission region, but later work developed the intrinsic absorption model where the cold gas is dispersed through it (Allen & Fabian 1997). Our spectral fits produce contour plots of mass cooling rate (Mdot) against intrinsic column density (⁠|$N_{\rm H}$|⁠). The allowed regions in most objects avoid (0, 0) in those plots, demonstrating that the absorbed emission model is a better fit than one without absorption.

Here, we re-analyse the cooling flow in the nearby Centaurus cluster (redshift |$z=0.0104$|⁠) using a smaller aperture for the XMM reflection grating spectrometer (RGS) data used than for the initial analysis presented in HCFI. We then briefly analyse spectral and imaging data of Centaurus using Chandra data.

We next compare our results on 29 clusters, groups, and elliptical galaxies, including those from 10 more clusters presented in the appendix, with mass cooling rates from Chandra imaging and star formation rates tabulated by McDonald et al. (2018). A picture emerges in which the hidden mass cooling rates (HCRs) are in approximate agreement with rates obtained from Chandra imaging (IMR), assuming an outer radius of the cooling flow corresponding to where the cooling time is 3 Gyr, provided neither rate exceeds |$15{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠. Higher values of IMR tend to have lower HCR by about a factor of 3 compared to the IMR until it exceeds |$100{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠. We propose in this paper that these trends are due to the effect of active galactic nucleus (AGN) feedback.

All cooling flows imply significant accumulations of cooled gas if they operate over several Gyr. The rate of normal star formation typically fails by a factor of about 20. We have addressed this issue in HCFI–III and returned to it in Fabian et al. (2024). Low-mass star formation is the most plausible solution (Fabian, Nulsen & Canizares 1982; Sarazin & O’Connell 1983; Fabian et al. 2024) and is briefly explored further in Section 5.1.

It is widely assumed in the literature that AGN feedback is efficient in heating intracluster gas so that no cooling flows occur (Mo, van den Bosch & White 2010). Here, we find that the efficiency in clusters ranges from 50 to 95 per cent. It appears to be much lower, i.e. it is inefficient, in elliptical galaxies and groups of galaxies.

2 THE CENTAURUS CLUSTER

2.1 The XMM RGS analysis

The RGS provides the spectrum from an effective slit of typically 90, 95, and 99 per cent in the cross-dispersion direction, corresponding to 0.8, 1.7, and 3.4 arcmin width. Sanders et al. (2008) show that for Centaurus most of the lines from low temperature gas are captured within the 90 per cent aperture. We therefore use that here. RGS 1 and 2 have dead chips covering 10.4–13.8 and 20–24 Å, respectively.

The corrected spectrum is shown in Fig. 1 with the best-fitting HCF model applied. The total model consists of Galactic absorption applied overall to a single temperature apec component plus a multilayer absorption model mlayerz [|$(1-\exp (-\sigma N_{\rm H}))/(\sigma N_{\rm H})]$|⁠, where |$\sigma$| is the photoelectric cross-section at the relevant energy and |$N_{\rm H}$| is the total column density) applied to a cooling flow model mkcflow. The higher temperature of the cooling flow is fixed to equal that of the single temperature component and the lower temperature is |$0.1{\rm \, keV}$|⁠. As the spectrum is from an extended object, Gaussian smoothing is applied separately to the two components. Fig. 1(a) shows the spectrum and best-fitting components. Fig. 2(b) shows the underlying cooling flow component without the multilayered absorption. It is clear that the cooling flow would have been immediately obvious in the first RGS observations had there been no excess absorption.

Fig. 2(a) shows the mass cooling rate (Mdot) as a function of the total column density |$N_{\rm H}$| and Fig. 2(b) shows Mdot versus covering fraction, which is mostly greater than 0.9. Fig. 2(c) shows the model absorbed spectra for three (⁠|$N_{\rm H}$|⁠, Mdot) pairs along the narrow best fitting region of Fig. 2(a). The three spectra are very similar above 12 Å. The divergence at shorter wavelengths is due to the absorption becoming optically thin. The behaviour above 12 Å is due to the mlayerz absorption approximating to a power law in energy as |$\sigma N_{\rm H}$| increases rather than the usual simple exponential characteristic of single-layer absorption.

If we were dealing with a perfect spectrum of the complete region out to several arcmin, then we can determine a single value of Mdot. However, we have a view that is restricted in a complicated manner. Instead, we rely on the far-infrared (FIR) emission detected by Herschel (Mittal et al. 2011) and equate that to the absorbed soft X-ray flux as discussed in HCFI, which gives an Mdot of about |$14{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| and |$N_{\rm H}\sim 10^{22}{{\rm \, cm}^{-2}\, }$|⁠.

The above model does not include the emission from the hot intracluster gas on the other side of the absorbing core. To accurately include this, we would need to know the extent and geometry of the absorbing material. In the absence of that knowledge, we assume that half of the apec component originates from the front and the other half is behind the core, absorbed by a total column density of |$N_{\rm H}$|⁠. The resulting backside emission is shown in green in Fig. 3 and has a negligible effect on the HCF above 13 Å. At shorter wavelengths, it can be confused with the uncertain emission from larger radii.

A final issue that we investigated is connected with the simplicity of the mlayerz model used on what is likely to be a very complex region. Is the absorption the same for all temperatures? In essence, we assume that the same complete cooling flow lies behind each interleaved layer of absorbing matter. To test this, we split the cooling flow model in two, the first part cooling from the outer temperature to a lower one, |$T_{\rm low}$| the second part then cooling from |$T_{\rm low}$| to 0.1 keV. |$\dot{M}$| is the same for both parts and |$N_{\rm H}$| allowed to be different. The resulting fit for |$\dot{M}$| versus the value of |$N_{\rm H}$| for the hotter flow is shown in Fig. 3(b). The value of |$N_{\rm H}$| for the cooler flow is 2.5 times larger. We checked for this effect in a few other clusters and found that it was not needed in 2A 0335+096 but did improve the fit for HCG62, where |$T_{\rm low}=0.35{\rm \, keV}$| was required. The overall value of |$\dot{M}$| is slightly reduced. Lastly, Fig. 3(c) shows the mass cooling rate as a function of abundance Z.

2.2 Chandra observations of the Centaurus cool core

Chandra has observed the Centaurus cluster several times (Crawford, Sanders & Fabian 2005a; Sanders et al. 2016). Using 280 ks of early data, taken in 2000–2004 when the absorption due to material built up on the optical blocking filter (Plucinsky, Bogdan & Marshall 2022) was minimal, we made a colour image of the core [Fig. 4(a) shows the ratio of hard (1.05–2 keV) to soft mid-band (0.65–0.95 keV) X-rays smoothed with a 2D Gaussian with sigma  = 5 arcsec]. The nucleus is marked by the pale cross. The Chandra spectrum of region 2 (with the nucleus excised) is shown in Fig. 4(b) and contours in the |$\dot{M}\!-\!N_{\rm H}$| plane are shown in Fig. 4(c).

The colour image shows where the multilayer absorption and emission is occurring as a darker colour compared with the lighter regions where it is minimal. It is not symmetrical and roughly matches the optical emission and absorption filamentation (see e.g. Fabian et al. 2017). The Chandra HCF rates for regions 1, 2, 3, 4, and 5 are 0.24, |$5.7\pm 0.45$|⁠, 1.65, 0.85, and |$\lt 0.03{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠, respectively. The abundance rises from 0.67 in region 2 to 1.5 for region 5. The pattern shows that any simple deprojection is not appropriate and we defer any detailed multilayer analysis of the Chandra data for now.

The dark patch in Fig. 4(a) also matches the low abundance region identified by Panagoulia, Fabian & Sanders (2013). Similar drops in central abundance were found and studied in other cool core clusters (Panagoulia, Sanders & Fabian 2015; Mernier et al. 2017; Lakhchaura, Mernier & Werner 2019; Liu, Zhai & Tozzi 2019). As discussed by Panagoulia et al. (2013), stellar mass-loss in the host galaxy should lead to central peaks in iron and other abundances. Drops in abundance were ascribed to outflows from ongoing feedback. Here, we suggest that dust grains swept into the ongoing cooling flows may be another part of the explanation for the drops. They will of course contribute to the intrinsic absorption. Some of the ‘missing iron mass’ of Panagoulia et al. (2013) may have been swept inward by the cooling flow.

3 EMISSION FROM GAS COOLING BELOW 2 MILLION K

X-ray emission from O vii in cool cores was found in stacked RGS spectra by Sanders & Fabian (2011). It was then studied in individual spectra of several elliptical galaxies by Pinto et al. (2016). The ratio of Fe xvii to O vii emission was larger then expected from simple cooling gas. A possible explanation for this result is that there is cold absorbing gas along our line of sight. The O vii doublet is at a wavelength just below the neutral O edge, so more sensitive to absorption. O vii emission from Centaurus was also reported by Fabian et al. (2016) at an implied level of about |$1{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠. This is likely due to the covering fraction not being exactly unity (Fig. 2b), with small open patches.

FUV emission from O vii, expected from gas at |$2.5\!-\!4\times 10^5\,\mathrm{ K}$| has been sought in cooling flows. As noted in HCFII, it was detected in the cluster A2597 by Oegerle et al. (2001) and using FUSE in the elliptical galaxy NGC4636 by Bregman, Miller & Irwin (2001). Re-analysis by Bregman et al. (2006) confirmed the A2597 result and revealed O vi emission in A1795 and the Perseus clusters. Lecavelier des Etangs, Gopal-Krishna & Durret (2004) found limits on two more clusters (AWM7 and A3112). A tight limit on O vi emission corresponding to |$\lt 10{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| was also found using a small aperture COS observation with HST in RXJ1532 by Donahue et al. (2017). On the contrary, McDonald et al. (2015) found O vi emission corresponding to |$\gt 1000{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| in the high-luminosity Phoenix cluster.

O vi emission was detected by Bregman et al. (2001) in the Virgo elliptical galaxy NGC4636 at a rate of |$0.43{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠. but gave only an upper limit of |$0.3{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| on NGC1404. HCF in the ellipticals M49 and M84 reported in HCFII at rates of 1 and |$2{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠, FIR detections (Temi et al. 2004, 2018)) and evidence of dust (e.g. Goudfrooij & de Jong 1995) fit a picture of small absorbed cooling flows operating there.

The overall results on O vi may appear confusing with detections in some objects but not others. They are however consistent with the HCF model in which some objects including A2597 (HCFIII, also see Morris & Fabian 2005) have unabsorbed components and A1795 (Section A3) having mass cooling rates consistent with the O vi fluxes. The dust extinction also appears patchy. The detections of O vi emphasize that the gas can continue to cool below |$10^6{\rm \, K}$| at a rate similar to that at higher X-ray emitting temperatures. As we shall see in the next section, MIR lines should be a better test of low temperature cooling.

4 NIR AND MIR FROM JWST: A DECISIVE TEST OF THE HIDDEN COOLING FLOWS FRAMEWORK

The cooling flow mystery is the question why the cooled gas is not detected in the soft X-ray band. The ‘HCFs’ model discussed here and in (Fabian et al. 2022, 2023a, b) proposes that gas does cool down, but that there are sources of soft X-ray opacity that absorb soft X-ray emission. The JWST infrared detectors can see through any such opacity, so they will detect the cooled gas if it exists. We are developing decisive spectral tests that will allow JWST to settle the matter.

Fig. 5 shows cloudy simulations of the spectrum of the Centaurus cluster cooling flow. Version 23.01 of cloudy is used (Chatzikos et al. 2023; Gunasekera et al. 2023).

JWST’s IR wavelength range of |$\sim 1$|–30 |$\mu$|m is shown. This model is speculative and is based on X-ray observations since the IR part of the spectrum has not yet been observed. The simulation follows a time-dependent non-equilibrium cooling flow starting with hot gas, |$T_{\rm kinetic}=3.4 \times 10^7 {\rm \, K}$|⁠, which is mainly emitting in the X-ray. It cools while maintaining constant gas pressure. Chatzikos et al. (2015) give computational details of cloudy’s treatment of a non-equilibrium cooling gas.

The microphysics in cloudy is solved for a cooling unit cell, a cube 1 cm on a side and the predictions are in units of emission per unit area of cooling flow. The results must be renormalized to account for the strength and distance of a real flow. Initially, we renormalize the spectrum (Table 1) to agree with the observed xspecmkcflow prediction of the Fe xvii 15A lines from a |$1{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| cooling flow at the distance of the Centaurus cluster of |$3.2\times 10^{-14}$| erg cm|$^{-2}$| s|$^{-1}$|⁠.

A key issue is how cool the gas becomes. Is it reheated, preventing any cold gas? Does it cool to temperatures where star formation is possible? Several spectra, with different lowest cooling flow temperatures |$T_{\rm {low}}$|⁠, are shown in Fig. 5. The infrared spectra are quite different; the simulations allowed to fully cool produce noticeably stronger low-ionization emission.

Fig. 6 shows the intensity ratio of a pair of low- and high-ionization iron lines. There are many such pairs in the infrared; this particular one was chosen as an example. It involves two lines of the same element, so the chemical composition need not be known. The high-ionization coronal line [Fe viii] forms in hot parts of the flow, whereas the [Fe ii] line forms in cooled gas. The panel shows the predicted line ratio as a function of the lowest temperature in the cooling flow. The intensity ratio changes by nearly 7 dex, showing that JWST can accurately determine the lowest temperature in the flow.

The simulations in the figure assumed that the gas maintained constant gas pressure as it cooled. Other equations of state (EOS) could be tested since JWST spectra reveal a wide range of ionization. The distribution of ionization states, for example, Fe x, Fe ix, Fe viii, etc., are sensitive to the EOS because it affects the density of the flow, its cooling rate, and hence the relative portion of each ion.

As an example, if magnetic pressure contributes to the EOS and we assume flux freezing with a chaotic field, the field will increase linearly with the density, and the magnetic pressure will vary as the square of the density. The field will increase as the flow cools until the magnetic pressure dominates and the flow becomes constant density rather than constant gas pressure. The spectrum of a constant gas pressure flow can be distinguished from the constant-density case if a range of ionization is observed. JWST can solve this problem.

Strong [Fe ii] lines are ubiquitous in Fig. 5 due to the relatively high abundance of Fe and the dense spacing of low-lying Fe|$^+$| energy levels. cloudy’s upgraded treatment of Fe ii emission is described in Sarkar et al. (2021). [Fe ii] emission is a hallmark of a cooling flow in the infrared.

The calculations assume that grains do not form in the cooling gas, so that iron remains in the gas phase throughout. Draine (2009) argues that a significant fraction of grains in our galaxy form within interstellar clouds rather than in stellar winds. Iron is heavily depleted when grains form (Jenkins 2009). Iron emission would become significantly fainter in regions where iron-bearing grains exist. This is a complication, but it is possible that JWST cooling-flow observations could shed insight into the circumstances where grain formation in diffuse clouds becomes important.

4.1 Ne vi

Ne vi emits a forbidden line at |$7.65\,\mu$|min the MIRI band that is produced by gas cooling over the temperature range of |$6\!-\!1.5\times 10^{5}{\rm \, K}$| (Fig. 7). Scaling to the flux predicted in Table 2, which is for a 0.55 solar abundance cooling flow of |$1{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| at the distance of the Centaurus cluster (⁠|$z=0.0104$|⁠), should enable MIRI observations of cooling flows to be tested. For a flow of |$1{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠, the luminosity of [Ne vi] |$\lambda 7.65\,\mu$|m is |$5\times 10^{36}{{\rm \, erg}{\rm \, s}^{-1}\, }$|⁠. For a |$14{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| steady cooling flow in Centaurus, we predict a [Ne vi] line flux of |$4\times 10^{-16}{{\rm \, erg}{\rm \, cm}^{-2}{\rm \, s}^{-1}\, }$|⁠. As a noble gas, Ne is not involved in grain formation, of course.

It will be important to know how spread out the coolest emission from the flow is. In HCFI, to make an approximate estimate of the volume of such gas, |$\Delta V$|⁠, we use the cooling equation:

Taking |$\Lambda =8\times 10^{-23}{{\rm \, erg}{\rm \, cm}^3{{\rm \, s}^{-1}\, }\, }$| (Lykins et al. 2013) for the total cooling function at the appropriate metallicity (about half solar) and temperature range (⁠|$\sim 5\times 10^5\,{\mathrm K}$|⁠), and pressure |$nT=10^{6.5}{{\rm \, cm}^{-3}{\rm \, K}}$|⁠, we find that |$\Delta V=2\times 10^{63}\dot{M}{{\rm \, cm}^3\, }$|⁠. (The factor of 5/2 will be 3/2 at constant density.) Assuming a sphere, the equivalent radius is then |$8{\dot{M}}^{1/3} {\rm \, pc}$|⁠. This will have reduced from |$200{\dot{M}}^{1/3}\, \mathrm{ pc}$| when the gas is at about |$5\times 10^6{\rm \, K}$|⁠, due to the rapidly rising density and increase in emissivity. Assuming that the |$14{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| cooling flow in Centaurus is steady and continuous means that [Ne vi] emission originates from a volume equivalent to a sphere of radius 20 pc. We do not know the geometry of the inner flow, which may be in many small clouds, sheets or filaments (as in the HST and Chandra images, Fig. 4a).

Detection and mapping of the Ne vi MIR line can validate the HCF model presented here. It can demonstrate whether or not the gas cools over three orders of magnitude in temperature from, say, 5 keV to 5 eV, in a continuous steady fashion or not.

As well as direct line emission from the cooling gas, there will be line emission from the surrounding gas irradiated by the cooling gas. The results of cloudy simulations of this process are published in the work of Polles et al. (2021). Near- and mid-infrared Spitzer spectra of filaments in the Centaurus and Perseus clusters have been reported by Johnstone et al. (2007).

5 THE EMERGING OVERALL PICTURE OF HIDDEN COOLING FLOWS

Including the objects in Appendix  A, with details in Tables 2, 3 and Figs 8–21, we now have mass cooling values for 38 clusters, groups, and elliptical galaxies. In all cases, the RGS spectra are consistent with and show better spectral fits with the simple HCF model. This has just three new parameters: total cooling rate |$N_{\rm H}$|⁠, Mdot, and covering fraction f (which just measures the partition between absorbed and unabsorbed cooling).

We now compare results of the 29 objects that have unabsorbed cooling flow estimates from Chandra imaging data published by (McDonald et al. 2018), here labelled IMR. (The excluded objects are nearby elliptical galaxies.) Such estimates require a fiducial cooling time which is less than 7 or 8 Gyr, on the assumption that the age of cluster cores, which are still forming, is at least the look back time to redshift |$z=1$|⁠. McDonald et al. (2018) argue for a shorter time of 3 Gyr based on the size of the associated optical nebulae. Their results include most of our galaxies and also give estimates of the star formation rate (SFR) due to normal star formation. References to the original measurements used are given in the tables of McDonald et al. (2018).

Before proceeding, we note that the IMR values are now at least four times less than the pre-2000 estimates due to the shorter cooling time (factor of |$\sim 2$| and the change in Hubble constant |$H_0$| from 50 to |$70 {{\rm \, km}\, {\rm \, s}^{-1}{\rm \, Mpc}^{-1}\, }$|⁠). There is however still an issue with the cooled gas mass which we addressed in depth in HCFI and here is Section 5.1.

Fig. 8 shows the HCR and SFR as a function of imaging rate IMR. The HCRs are mostly consistent with the IMR when they are less than about |$15{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠, which is where the elliptical galaxies and many groups lie. From IMR rates of 15–|$300{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠, the HCRs lie about a factor of several below. This is the range for regular rich clusters where AGN feedback may be reducing the cooling in the outer parts of the cool core, mainly beyond the bubbles. The HCRs then increase back close to the line at higher cooling rates. The SFRs all lie below the HCRs.

This is emphasized in the lower panel of Fig. 8 where the ratio of IMR/HCR is plotted against IMR. Ignoring the point on the lower left, which is the Virgo elliptical galaxy M84, the objects with IMR less than 10 roughly have equal values of IMR and HCR (IMR/HCR  = 1). Above IMR of 10 the mean ratio is 5.8, but there is a wide spread of values. As suggested above, this could be the action of AGN feedback. We note that the mass deposition rate of cooling flows determined from early imaging analyses generally showed |$\dot{M} \propto r$|⁠, where r is the radius (see e.g. Fabian et al. 1994). The aperture used for the RGS spectra are typically much smaller than that used for imaging measurements of cooling rate (it also depends on source distance).

We summarize the results for 12 clusters with imaging rates greater than |$15{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| and where |${\rm IMR}\gt {\rm HCR}$| in Fig. 8. Here, we define the percentage radiative efficiency as |$100 \times (1-{\rm HCR}/{\rm IMR}).$| This is then plotted against the imaging rate |${\rm IMR}.$| It shows that the efficiency of AGN feedback exceeds 50 per cent for many clusters. There is however a significant fraction of massive clusters that appear immune to feedback heating. This could be intrinsic or a time-dependent behaviour. We find no simple correlation between the above feedback efficiency and the position of a cluster in the cavity power–cooling luminosity plane (e.g. Rafferty et al. 2006; Hlavacek-Larrondo et al. 2012).

In practice, assuming a universal cooling age of 3 Gyr may be inappropriate. If too short then the values of IMR are underestimates. If so, then the feedback efficiencies will increase and vice versa if the age is too long. The values, especially for the extreme clusters with very high cooling rates may also change over time, sometimes abruptly if the central AGN has large increases in its power (e.g. H1821 + 643; Russell et al. 2024).

The viability of jetted feedback to completely cancel soft X-ray cooling is highly unlikely. Heating by jets and bubbles principally occurs at and beyond the ends of jets.

5.1 Low-mass star formation

We attribute the lack of any normal star formation in most cooling flows, despite substantial mass cooling rates, to low-mass star formation (e.g. HCFI; Fabian et al. 2024). High-pressure, typical of cooling flows (⁠|$nT\gt 10^{6.5}{{\rm \, cm}^{-3}{\rm \, K}\, }$|⁠), leads to a low Jeans mass (⁠|$\sim 0.01{\rm \, {\rm M}_{\odot }}$| and therefore low-mass protostars; Jura 1977; Fabian et al. 1982; Sarazin & O’Connell 1983; Ferland, Fabian & Johnstone 1994). Elliptical galaxies, such as the hosts of cooling flows, are observed to have a bottom-heavy initial mass function (IMF; van Dokkum & Conroy 2010; Mehrgan et al. 2019; Gu et al. 2022; van Dokkum & Conroy 2024). These issues are probably coupled.

The development of an IMF is due to accretion of surrounding gas on to protostars (Krumholz et al. 2016). As explained in that paper, in order to remain low mass and give a bottom-heavy IMF, further accretion needs to be stopped or disrupted. This may naturally happen at the centres of elliptical galaxies where the stellar number density and velocity dispersion are both very high. Fast interactions with the numerous low-mass stars and protostars could be responsible for stopping further accretion. We suggest that, in this way, the IMF from the cooled material may accumulate into a peaked distribution of objects centred on the Jeans mass.

6 CONCLUSIONS

The further analyses presented here show that the general picture for Centaurus is robust. Soft X-ray cooling is spread over the inner 30 arcsec, approximately where absorption is seen in optical images and coincident with the central drop in iron abundance.

JWST observations of the centres of cool cores will allow decisive checks of further cooling of gas to |$10^5{\rm \, K}$| and below. Of particular note is the detection and mapping of MIR emission [Ne vi] at |$7.65\, \mu$|m.

The current set of 38 objects shows that absorbed cooling flows are common. The operation of AGN feedback reduces cooling of outer gas near and beyond the bubbles in more than 50 per cent of cooling core clusters. At the same time, soft X-ray cooling persists in the innermost regions of all cool cores in clusters, groups, and elliptical galaxies.

The overall lack of normal star formation in these innermost regions can be explained by a mode of low-mass star formation. This contributes to the bottom-heavy initial mass function now commonly inferred for the central parts of massive elliptical galaxies.

ACKNOWLEDGEMENTS

ACF acknowledges a discussion with Mark Krumholz.

DATA AVAILABILITY

All data presented here are available on the XMM and Chandra archives.

REFERENCES

APPENDIX: FURTHER COOL CORE CLUSTERS AND GROUPS.

A Details of Objects and Data are given in Table 3

A1 HCG62

Hickson Compact Group 62 (Fig. 10) is X-ray luminous. It has been well observed with Chandra (Morita et al. 2006; Rafferty et al. 2013) and shows a cool core disturbed by shocks or more likely a cold front due to a merger. Cavities in the X-ray emission caused by a central jetted radio source are evident. No recent star formation has been reported.

A2 A3581

A3581 (Fig. 11) hosts the most luminous cool core of any nearby group and shows active radio mode feedback in the from of bubbles from the supermassive black hole in its BGG, IC 4374. Chandra observations are discussed in detail by Canning et al. (2013). Multiple outbursts are inferred to have occurred. No young stars are seen except in a star cluster.

A3 A1795

The X-ray cool core cluster A1795 (FIg. 12) has a 46 kpc long cool X-ray filaments extending 46 kpc to the South of the BCG (Crawford et al. 2005b), which represents the peak of soft X-ray emission. Further Chandra data (it is a Chandra calibration source) are discussed by (Ehlert et al. 2015). Star formation is occurring in the long filament. RGS spectra are presented by Tamura et al. (2001). Our RGS results show that there is both a modest unabsorbed cooling flow of about |$17{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| together with a possibly much larger hidden flow.

A4 Cygnus A

The famous radio galaxy Cygnus A (Fig. 13) ies at the centre of a cool core cluster of galaxies. Chandra data of the nuclear region were presented by Young et al. (2002), revealing an AGN absorbed by a column density of |$N=10^{23}{{\rm \, cm}^{-2}\, }$|⁠. This means negligible X-ray emission from the nucleus in the RGS band used here. A dust lane is seen across the centre (Riffel 2021; Carilli et al. 2022). The plot of column density versus mass cooling rate was made with unit covering fraction.

A5 A1664

Chandra data on A1664 (Fig. 14) are presented by Calzadilla et al. (2019). Liu et al. (2021) analyse the RGS data of A1664. The ALMA molecular mass is |$10^{10}\,\hbox{M}_{\odot }.$|

A6 RXJ1504

RXC J1504.1−0248 (Fig. 15) is a high-luminosity massive cluster with a bright cool core accounting for 70 per cent of its X-ray luminosity (Böhringer et al. 2005). Chandra observations are discussed by Vantyghem et al. (2018) together with ALMA and HST data revealing |$2\times 10^{10}{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| of molecular gas and a system of dusty filaments. Ogrean et al. (2010) find a star formation rate of |$136{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| from GALLEX UV data. Liu et al. (2021) analysed the RGS X-ray spectrum and deduced a hidden cooling flow rate of |$520\pm 30{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$|⁠.

A7 A1068

Chandra data of A 1068 (Fig. 16) are presented in Wise, McNamara & Murray (2004), with further analysis by Rafferty, McNamara & Nulsen (2008). Edge et al. (2010) present Herschel FIR data and give a CO gas mass of |$4.1\times 10^{10}{\rm \, {\rm M}_{\odot }}$|⁠. The plot of column density versus mass cooling rate was made with unit covering fraction.

A8 Hydra A

Hydra A (Fig. 17) was Observed by Chandra (McNamara et al. 2000; Gitti et al. 2011). Olivares et al. (2019) give a molecular mass of |$5.5\times 10^9{\rm \, {\rm M}_{\odot }}.$| Rose et al. (2019) find molecular absorption in the form of a dense disc.

A9 A3112

The cool core cluster A3112 (Fig. 18) has been discussed by Calzadilla et al. (2022), Quillen et al. (2008), and Rose et al. (2019).

A10 NGC533

NGC533 (Fig. 19) is a massive elliptical galaxy at a distance of about 70 Mpc, at the centre of a group or poor cluster, sometimes confused with the more distant cluster A189.

It was studied by Peterson et al. (2003) in a cooling flow study of 14 objects observed with the XMM RGS. A cooling flow model was fitted to successive temperature intervals showing that Mdot dropped from |$5\pm 0.4{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| to values consistent with zero below 0.4 keV. No intrinsic absorption was considered. Lakhchaura et al. (2018) have deprojected the Chandra data to find that the radiative cooling time within the central 600 pc is 30 Myr. The luminosity of H |$\alpha$| emission is |$3.24 \times 10^{40}{{\rm \, erg}{\rm \, s}^{-1}\, }$| (Macchetto et al. 1996). Grossová et al. (2022) show radio emission contours revealing a low-power FRII double source with lobes E–W at radii of 1 kpc.

Our RGS analysis (Fig. 9) yields an excellent fit to a mass cooling rate of about |$12{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| with intrinsic absorption of |$1.2\times 10^{22}{{\rm \, cm}^{-2}\, }$|⁠.

Gu et al. (2022) have studied the stellar IMF in the centre of 41 massive early-type galaxies, including NGC533. All have an IMF steeper than a Milky Way (MW, Kroupa) IMF, i.e. a bottom heavy IMF. NGC533 requires, within its innermost 4 kpc radius, a mass to light ratio |$74\pm 0.15$| per cent larger than would be expected from an MW IMF. This could be the repository for much of the cooled gas.

A11 A1835 and the Perseus cluster

These massive cool core clusters were discussed in HCFI and are shown again here (Figs 20 and 21) with clearer spectra The analysis of the Perseus cluster shown in HCFI (Fig. 5a) allowed a maximum value of |$N_{\rm H}$| of |$5\times 10^{22} {{\rm \, cm}^{-2}\, }$|⁠. Extending that limit to |$10^{23}{{\rm \, cm}^{-2}\, }$| allows higher values of Mdot (Fig. 5b). The high FIR luminosity from the cluster means that we have no strong soft X-ray constraint on the total level of cooling. The values found from Chandra of |$\sim 400{{\rm \, {\rm M}_{\odot }}{\rm \, yr}^{-1}\, }$| are possible.