Spin Demographics of Active Supermassive Black Holes: Updated Estimates from X-Ray Reflection and Future Opportunities

1. Introduction

The no-hair theorem of General Relativity states that astrophysical (uncharged) black holes are described by two fundamental quantities: black hole mass, $M_{\mathrm{BH}}$ and angular momentum, $\mathbf{J}$, or spin. The spin is commonly expressed as a dimensionless parameter $a^{*}$$=c\mathbf{J}/G_{\mathrm{N}}{M}_{\mathrm{BH}}^2$, where c is the speed of light in the vacuum and $G_{\mathrm{N}}$ is Newton’s gravitational constant. For a Kerr (spinning) black hole, $a^{*}$ must be within $\pm 1$, where negative (positive) values of $a^{*}$ denote orbits that are counter-rotating (co-rotating) with respect to the black hole spin. As first demonstrated by Ref. [3], a hole spun up by prolonged prograde accretion will inevitably be spun down by the capture of counter-rotating photon orbits, imposing the canonical upper limit on the spin magnitude of a Kerr black hole of $a^{*}$$=+0.998$.

In addition to being a fundamental property, the spins of supermassive black holes (SMBHs) in active galactic nuclei (AGN) act as fossil records of SMBH growth. One key question is the coherence of the angular momentum of inflowing material as the SMBH grows. In some semi-analytic models (SAMs) of hierarchical structure formation, SMBHs with $\log (M_{\mathrm{BH}}/M_{\odot })\lesssim 8$ primarily grow via ordered or coherent accretion via thin-disks, leading to high-spin SMBHs in galaxies like the Milky Way [11,49]. Other SAMs also show that a prolonged phase of incoherent gas accretion would spin black holes down [39]. For instance, Ref. [21] showed that late-time incoherent (chaotic) accretion will lower the average spin of SMBHs in local AGN across mass scales. Since the characteristic spin-up and spin-down timescales in SAMs are frequently sensitive to the physical (rather than Eddington) accretion rate $\dot{m}$, transitions between radiatively inefficient and efficient accretion modes can further accelerate or suppress this mass–spin evolution [77,120].

For SMBHs with magnetized accretion flows, spin can also be decreased as spin energy is transformed into jet power via the Blandford Znajek (BZ) mechanism [4,34,103,114]. By fitting General Relativistic Magnetohydrodynamics (GRMHD) simulations, Ref. [110] proposed a model in which significant spin-down occurs whenever the disk becomes geometrically thick, at either highly sub-Eddington or super-Eddington accretion rates. These formulae were then placed in a SAM demonstrating observationally testable spin moderation via this process even when accretion proceeds in a purely coherent fashion [127]. Exploring the magnitude of BZ-driven spin-down in different simulation setups is an active area of research. Using GRMHD simulations with radiative cooling, Ref. [123] proposed a universal equilibrium spin value of $a^{*}\approx 0.3$ for luminous strongly magnetized accretion flows. Meanwhile, using multi-zone GRMHD simulations from the event horizon to the Bondi radius, Ref. [129] find less constant jets, and therefore longer equilibrium timescales than Refs. [103,110] by a factor of a few.

Over the past decade, hydrodynamical simulations of cosmic structure formation have started incorporating sub-grid prescriptions to account for SMBH spin evolution. Recently, Ref. [118] ran a cosmological simulation with OpenGadget3 code using a novel sub-resolution prescription to track the black hole spin by accounting for the effects of coalescence and misaligned accretion through a geometrically thin, optically thick accretion disk. Ref. [118] found that low-mass holes ($M_{\mathrm{BH}}<{10}^7{M}_{\odot }$) grow primarily through gas accretion, occurring mostly in a coherent fashion that favors spin-up. At higher masses ($M_{\mathrm{BH}}>{10}^7{M}_{\odot }$), the gas angular momentum directions of subsequent accretion episodes were often found to be uncorrelated. A high level of correlation between counter-rotating accretion and black hole spin-down was thus inferred at masses $>{10}^7{M}_{\odot }$ – a regime where SMBH coalescence was also identified to be an important growth channel. Overall, Ref. [118] concluded that the spin distributions from their simulation display a wide variety of histories, depending on the dynamical state of the gas feeding the black hole and the relative contribution of mergers and gas accretion. Other state-of-the-art numerical models also highlight that the efficiency of spin evolution is strongly tied to the instantaneous accretion rate: at fixed $\dot{m}$, low-mass SMBHs can undergo rapid spin-up on short timescales, whereas massive SMBHs require substantially longer periods of sustained coherent inflow to appreciably change their spin [120].

Here we outline the prospects of utilizing observed SMBH mass–spin populations with current and future samples to test predictions of SMBH growth from SAMs and hydrodynamic simulations, where spins estimates are drawn from X-ray reflection spectroscopy. These reflection-based estimates are expected to trace the innermost flow onto holes whose surrounding accretion disks are geometrically thin and optically thick in the Shakura-Sunyaev regime [1,2]. Therefore, we do not consider spin estimates based on other methods1. We have made the set of archival SMBH mass and reflection-inferred spin estimates compiled here publicly available on GitHub to enable continuous updates as new constraints become available or existing ones are revisited. A full quantitative analysis of the spin–mass distribution, including forward-modeling and population-level inference, will be presented in a separate contribution within a NewAthena Special Issue under preparation for publication in JHEAP.

Our contribution is organized as follows. In Section 2, we present the updated SMBH mass–spin sample with reflection-inferred spins compiled from the literature, together with several ancillary quantities of interest – including redshift, Eddington ratio and X-ray luminosity ($2-10\mathrm{keV}$ observed frame). We then interpret this observed mass–spin plane and find no obvious correlation between the Eddington-scaled accretion rate and the black hole spin. We then outline the caveats associated with using the current observed mass–spin sample to test predictions of SMBH growth models which predict that accretion-driven and accretion+merger-driven growth would imprint different expected trends in the mas–spin plane. The caveats we highlight arise from the present limitations in sample size, heterogeneity, and statistical and systematic uncertainties. Considering the heterogeneity of reflection-based spin inference in the current literature we then argue that hierarchical Bayesian inference approaches hold a promising pathway to confirming the presence of possible mass–spin trends in observed populations. Finally, we introduce NewAthena’s encouraging prospects in enabling such an assessment.

NewAthena is the European Space Agency’s next-generation flagship-class X-ray observatory, planned for launch in 2037 with unprecedented survey and spectroscopic capabilities [131,132,133,134,135]. With its large collecting area ($1-1.4{\mathrm{m}}^2$ at 1 keV), broad bandpass ($0.1-12\mathrm{keV}$), and the exceptional spectral resolution of its X-IFU microcalorimeter ($<5\mathrm{eV}$), NewAthena will resolve broad and narrow reflection features in the iron K band of nearby AGN that could be degenerate with relativistically smeared reflection. NewAthena will also extend reflection-based spin inference into a high redshift regime ($z\lesssim 1.5$) in distant AGN whose Fe K band is redshifted into NewAthena’s bandpass. NewAthena’s strategic survey of at least 50 new nearby SMBHs is expected to deliver the pathway towards a robust observational discrimination between accretion-driven versus accretion+merger-driven growth from observed mass–spin trends in the local universe.

2. The Observed SMBH Mass vs. Spin Plane with Reflection-Inferred Spins

The spin vs. mass plane for most moderately accreting SMBHs with existing spin estimates from X-ray reflection spectroscopy – compiled from published journal articles at the time of writing – is shown in Figure 1. This suggests a tentative decrease in spin at masses $>{10}^8{M}_{\odot }$, which may be indicative of merger-driven growth. In contrast, a distinct low-mass (${10}^{6-7}{M}_{\odot }$) population of SMBHs with high-to-maximal spins ($a^{*}$$\sim 0.998$) seems to emerge, suggestive of coherent-accretion-driven growth [89,120]. This potential trend is illustrated by the gray arrow in Figure 1. If not solely the result of selection effects, the absence of retrograde spins in the current sample may place meaningful constraints on the contribution of prolonged chaotic accretion – as this would yield a broader mass–spin distribution (including retrograde values). This absence is also indicative of the important role of coherent accretion in driving SMBH growth. The exclusion of maximal spin values at 90% confidence in several SMBHs indicate that these SMBH are spun down by other processes, e.g. mergers.

Figure 1. Observed SMBH mass–spin plane with reflection-inferred spins compiled from published literature (data listed in Table 1; error bars in spin and mass show the 90% and 68% confidence levels, respectively). The plane comprises: 10 (red) and 28 (blue) SMBHs with well-defined vs. lower spin bounds updated from the spin reviews in Refs. [88,94]; and 13 low-mass AGN (green) presented in Ref. [102]. The gray arrow marks the expectation from theory, as described in the text.

Figure 1. Observed SMBH mass–spin plane with reflection-inferred spins compiled from published literature (data listed in Table 1; error bars in spin and mass show the 90% and 68% confidence levels, respectively). The plane comprises: 10 (red) and 28 (blue) SMBHs with well-defined vs. lower spin bounds updated from the spin reviews in Refs. [88,94]; and 13 low-mass AGN (green) presented in Ref. [102]. The gray arrow marks the expectation from theory, as described in the text.

Table 1. Spin as a function of mass for 38 SMBHs from an updated literature compilation of Ref. [94] (where the first 10 rows distinguish those with well-defined spin estimates), combined with the 13 low-mass AGN with X-ray-reflection-inferred spins from Ref. [102] (shown in the last 13 rows; see table 1 of Ref. [102] for each source’s full name). Rows are ordered by decreasing mass. The error bars in mass and spin correspond to the 90% and 68% statistical uncertainties, respectively. The third column in the table references the respective papers from which we quote the mass and spin estimates for each source. The last column indicates the optical spectral classification, where we make use of the following abbreviations: Rq: radio-quiet – Ri: radio-intermediate – Q: quasar – 1 (2) : type-1 (type-2) – Sy: Seyfert – BLRG: broad-line radio galaxy – NL: narrow-line – Lensed: gravitationally lensed – BAL: broad-absorption-line.

Source	${\mathit{M}}_{\mathbf{BH}}\left[{10}^6{\mathit{M}}_{\odot }\right]$	Spin ${\mathit{a}}^{*}$	Refs.	Type
H 1821+643††	$(3.0_{-1.5}^{+1.5})\times {10}^3$	$0.{62}_{-0.37}^{+0.22}$	[63,105]	RqQ,1
Q 2237+305††	$(1.2_{-0.6}^{+0.6})\times {10}^3$	$0.{76}_{-0.03}^{+0.06}$	[48,91]	Lensed Q,1
Fairall 9†	${255}_{-56}^{+56}$	$0.{71}_{-0.09}^{+0.08}$	[10,36]	NL,Sy,1
Ark 120†	${150}_{-19}^{+19}$	$0.{64}_{-0.06}^{+0.32}$	[10,79]	Sy1
RX J1131-1231†	$140\pm 70$	$0.{87}_{-0.15}^{+0.08}$	[50,50]	Lensed Q,1
IRAS 09149–6206*	$(1.0_{-0.5}^{+0.5})\times {10}^2$	$0.{94}_{-0.07}^{+0.02}$	[64,80]	Sy1
PG 1229+204†	${57}_{-25}^{+25}$	$0.{93}_{-0.02}^{+0.06}$	[10,78]	Sy1
Swift J2127.4+5654	$15.0_{-7.5}^{+7.5}$	$0.{72}_{-0.20}^{+0.14}$	[64,78]	Sy1
NGC 5506	$5.1_{-1.18}^{+1.18}$	$0.{93}_{-0.04}^{+0.04}$	[24,74]	NL,Sy1
Mrk 359’	$1.{10}_{-0.55}^{+0.55}$	$0.{66}_{-0.54}^{+0.30}$	[13,42]	NL,Sy1
PG 1426+015†	$(1.0_{-0.3}^{+0.3})\times {10}^3$	$>0.70$	[10,128]	Rq,Sy1
PG 2112+059	$(1.0_{-0.2}^{+0.2})\times {10}^3$	$>0.83$	[16,29]	BAL,Q
PG 0804+761’	${550}_{-60}^{+60}$	$>0.97$	[13,78]	Rq,1
1 H0419-577	${340}_{-170}^{+170}$	$>0.98$	[26,70]	Rq,Sy1
Mrk 1501††	${184}_{-27}^{+27}$	$>0.97$	[35,81]	Ri,1
RBS 1124†	${180}_{-90}^{+90}$	$>0.236$	[10,115]	Rq,Q
Fairall 51	$(1.0_{-0.5}^{+0.5})\times {10}^2$	$>0.6$	[14,57]	Sy1
Mrk 841	${79}_{-40}^{+40}$	$>0.52$	[13,42]	Rq,Sy1
IRAS 13197-1627’	${64}_{-34}^{+34}$	$>0.7$	[13,75]	Sy1.8
3C 120†	${60}_{-31}^{+31}$	$>0.95$	[10,40]	BLRG
Mrk 79†	$52.4_{-14.4}^{+14.4}$	$>0.5$	[10,78]	Sy1.2
IRAS 0521–7054’	${50}_{-10}^{+10}$	$>0.77$	[86,86]	Sy2
NGC 4151†	${50}_{-10}^{+10}$	$>0.9$	[54,97]	Sy1.5
1 H0323+342†	${34}_{-9}^{+9}$	$>0.9$	[65,68]	NL,Sy1
ESO 033-G002’	$31.6_{-7.9}^{+7.9}$	$>0.96$	[96,96]	Rq,Sy2
NGC 3783*	$25.4_{-7.2}^{+9.0}$	$>0.88$	[33,87]	BAL,Sy1
Mrk 110†	$25.1_{-6.1}^{+6.1}$	$>0.89$	[10,78]	NL,Sy1
Mrk 335†	$17.8_{-4.0}^{+4.0}$	$>0.91$	[10,55]	NL,Sy1
PG 1535+547	$14.8_{-7.2}^{+7.2}$	$>0.99$	[90,130]	NL,Sy1
ESO 362-G18	$12.5_{-4.5}^{+4.5}$	$>0.92$	[43,43]	Sy1.5
Tons 180’	$8.1_{-4.0}^{+4.0}$	$>0.98$	[13,78]	NL,Sy1
IRAS 13224-3809’	$6.3_{-3.0}^{+3.0}$	$>0.975$	[13,69]	NL,Sy1
1 H0707-495’	$3.0_{-1.0}^{+1.0}$	$>0.97$	[13,32]	NL,Sy1
MCG–06-30-15†	$2.9_{-1.6}^{+1.6}$	$>0.65$	[58,121]	NL,Sy1
Mrk 1044	$2.{82}_{-0.73}^{+0.90}$	$>0.9$	[53,71]	NL,Sy1
Ark 564	$2.3_{-1.3}^{+2.6}$	$>0.9$	[78,101]	NL,Sy1
NGC 1365	$2.0_{-1.0}^{+1.0}$	$>0.97$	[25,52]	Sy1.5-1.8
Mrk 766’	$1.8_{-0.5}^{+0.5}$	$>0.92$	[13,67]	NL,Sy1
J0107††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.87}_{-0.24}^{+0.08}$	[17,102]	NL,Sy1
J0940††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.996}_{-0.015}^{+0.001}$	[17,102]	NL,Sy1
J1357††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.35}_{-0.09}^{+0.15}$	[17,102]	NL,Sy1
J1541††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.91}_{-0.21}^{+0.07}$	[17,102]	BL,Sy1
J1559††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	$>0.975$	[17,102]	NL,Sy1
J1140††	${10}^{-1}\times (12.6_{-6.3}^{+12.5})$	${0.975}_{-0.016}^{+0.012}$	[17,102]	NL,Sy1
J1347††	${10}^{-1}\times (10.0_{-5.0}^{+10.0})$	${0.77}_{-0.43}^{+0.19}$	[17,102]	NL,Sy1
J1434††	${10}^{-1}\times (6.3_{-3.1}^{+6.3})$	${0.63}_{-0.45}^{+0.27}$	[17,102]	Sy1
J1631††	${10}^{-1}\times (6.3_{-3.1}^{+6.3})$	${0.76}_{-0.19}^{+0.16}$	[17,102]	BL,Sy1
J1023††	${10}^{-1}\times (5.0_{-2.5}^{+5.0})$	${0.53}_{-0.15}^{+0.39}$	[17,102]	NL,Sy1
J1626††	${10}^{-1}\times (5.0_{-2.5}^{+5.0})$	${0.68}_{-0.21}^{+0.28}$	[17,102]	Sy1.5
J0228††	${10}^{-1}\times (3.2_{-1.6}^{+3.1})$	${0.82}_{-0.09}^{+0.16}$	[17,102]	BL,Sy1
POX 52††	${10}^{-1}\times (3.2_{-1.6}^{+3.1})$	${0.56}_{-0.46}^{+0.36}$	[22,102]	Sy1.8

¹ Black hole mass estimated via: optical reverberation mapping^†; $H\alpha$, $H\beta$ or $C\mathtt{IV}$ widths, combined with a subsequent fit of virial scaling relations^††; VLTI GRAVITY interferometry*; an empirical method based on observed correlations between the equivalent width attributed to narrow-line 6.4 Fe K$\alpha$ emission’; and other methods (no symbol).

Table 1. Spin as a function of mass for 38 SMBHs from an updated literature compilation of Ref. [94] (where the first 10 rows distinguish those with well-defined spin estimates), combined with the 13 low-mass AGN with X-ray-reflection-inferred spins from Ref. [102] (shown in the last 13 rows; see table 1 of Ref. [102] for each source’s full name). Rows are ordered by decreasing mass. The error bars in mass and spin correspond to the 90% and 68% statistical uncertainties, respectively. The third column in the table references the respective papers from which we quote the mass and spin estimates for each source. The last column indicates the optical spectral classification, where we make use of the following abbreviations: Rq: radio-quiet – Ri: radio-intermediate – Q: quasar – 1 (2) : type-1 (type-2) – Sy: Seyfert – BLRG: broad-line radio galaxy – NL: narrow-line – Lensed: gravitationally lensed – BAL: broad-absorption-line.

Source	${\mathit{M}}_{\mathbf{BH}}\left[{10}^6{\mathit{M}}_{\odot }\right]$	Spin ${\mathit{a}}^{*}$	Refs.	Type
H 1821+643††	$(3.0_{-1.5}^{+1.5})\times {10}^3$	$0.{62}_{-0.37}^{+0.22}$	[63,105]	RqQ,1
Q 2237+305††	$(1.2_{-0.6}^{+0.6})\times {10}^3$	$0.{76}_{-0.03}^{+0.06}$	[48,91]	Lensed Q,1
Fairall 9†	${255}_{-56}^{+56}$	$0.{71}_{-0.09}^{+0.08}$	[10,36]	NL,Sy,1
Ark 120†	${150}_{-19}^{+19}$	$0.{64}_{-0.06}^{+0.32}$	[10,79]	Sy1
RX J1131-1231†	$140\pm 70$	$0.{87}_{-0.15}^{+0.08}$	[50,50]	Lensed Q,1
IRAS 09149–6206*	$(1.0_{-0.5}^{+0.5})\times {10}^2$	$0.{94}_{-0.07}^{+0.02}$	[64,80]	Sy1
PG 1229+204†	${57}_{-25}^{+25}$	$0.{93}_{-0.02}^{+0.06}$	[10,78]	Sy1
Swift J2127.4+5654	$15.0_{-7.5}^{+7.5}$	$0.{72}_{-0.20}^{+0.14}$	[64,78]	Sy1
NGC 5506	$5.1_{-1.18}^{+1.18}$	$0.{93}_{-0.04}^{+0.04}$	[24,74]	NL,Sy1
Mrk 359’	$1.{10}_{-0.55}^{+0.55}$	$0.{66}_{-0.54}^{+0.30}$	[13,42]	NL,Sy1
PG 1426+015†	$(1.0_{-0.3}^{+0.3})\times {10}^3$	$>0.70$	[10,128]	Rq,Sy1
PG 2112+059	$(1.0_{-0.2}^{+0.2})\times {10}^3$	$>0.83$	[16,29]	BAL,Q
PG 0804+761’	${550}_{-60}^{+60}$	$>0.97$	[13,78]	Rq,1
1 H0419-577	${340}_{-170}^{+170}$	$>0.98$	[26,70]	Rq,Sy1
Mrk 1501††	${184}_{-27}^{+27}$	$>0.97$	[35,81]	Ri,1
RBS 1124†	${180}_{-90}^{+90}$	$>0.236$	[10,115]	Rq,Q
Fairall 51	$(1.0_{-0.5}^{+0.5})\times {10}^2$	$>0.6$	[14,57]	Sy1
Mrk 841	${79}_{-40}^{+40}$	$>0.52$	[13,42]	Rq,Sy1
IRAS 13197-1627’	${64}_{-34}^{+34}$	$>0.7$	[13,75]	Sy1.8
3C 120†	${60}_{-31}^{+31}$	$>0.95$	[10,40]	BLRG
Mrk 79†	$52.4_{-14.4}^{+14.4}$	$>0.5$	[10,78]	Sy1.2
IRAS 0521–7054’	${50}_{-10}^{+10}$	$>0.77$	[86,86]	Sy2
NGC 4151†	${50}_{-10}^{+10}$	$>0.9$	[54,97]	Sy1.5
1 H0323+342†	${34}_{-9}^{+9}$	$>0.9$	[65,68]	NL,Sy1
ESO 033-G002’	$31.6_{-7.9}^{+7.9}$	$>0.96$	[96,96]	Rq,Sy2
NGC 3783*	$25.4_{-7.2}^{+9.0}$	$>0.88$	[33,87]	BAL,Sy1
Mrk 110†	$25.1_{-6.1}^{+6.1}$	$>0.89$	[10,78]	NL,Sy1
Mrk 335†	$17.8_{-4.0}^{+4.0}$	$>0.91$	[10,55]	NL,Sy1
PG 1535+547	$14.8_{-7.2}^{+7.2}$	$>0.99$	[90,130]	NL,Sy1
ESO 362-G18	$12.5_{-4.5}^{+4.5}$	$>0.92$	[43,43]	Sy1.5
Tons 180’	$8.1_{-4.0}^{+4.0}$	$>0.98$	[13,78]	NL,Sy1
IRAS 13224-3809’	$6.3_{-3.0}^{+3.0}$	$>0.975$	[13,69]	NL,Sy1
1 H0707-495’	$3.0_{-1.0}^{+1.0}$	$>0.97$	[13,32]	NL,Sy1
MCG–06-30-15†	$2.9_{-1.6}^{+1.6}$	$>0.65$	[58,121]	NL,Sy1
Mrk 1044	$2.{82}_{-0.73}^{+0.90}$	$>0.9$	[53,71]	NL,Sy1
Ark 564	$2.3_{-1.3}^{+2.6}$	$>0.9$	[78,101]	NL,Sy1
NGC 1365	$2.0_{-1.0}^{+1.0}$	$>0.97$	[25,52]	Sy1.5-1.8
Mrk 766’	$1.8_{-0.5}^{+0.5}$	$>0.92$	[13,67]	NL,Sy1
J0107††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.87}_{-0.24}^{+0.08}$	[17,102]	NL,Sy1
J0940††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.996}_{-0.015}^{+0.001}$	[17,102]	NL,Sy1
J1357††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.35}_{-0.09}^{+0.15}$	[17,102]	NL,Sy1
J1541††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	${0.91}_{-0.21}^{+0.07}$	[17,102]	BL,Sy1
J1559††	${10}^{-1}\times (16.0_{-8.0}^{+16.0})$	$>0.975$	[17,102]	NL,Sy1
J1140††	${10}^{-1}\times (12.6_{-6.3}^{+12.5})$	${0.975}_{-0.016}^{+0.012}$	[17,102]	NL,Sy1
J1347††	${10}^{-1}\times (10.0_{-5.0}^{+10.0})$	${0.77}_{-0.43}^{+0.19}$	[17,102]	NL,Sy1
J1434††	${10}^{-1}\times (6.3_{-3.1}^{+6.3})$	${0.63}_{-0.45}^{+0.27}$	[17,102]	Sy1
J1631††	${10}^{-1}\times (6.3_{-3.1}^{+6.3})$	${0.76}_{-0.19}^{+0.16}$	[17,102]	BL,Sy1
J1023††	${10}^{-1}\times (5.0_{-2.5}^{+5.0})$	${0.53}_{-0.15}^{+0.39}$	[17,102]	NL,Sy1
J1626††	${10}^{-1}\times (5.0_{-2.5}^{+5.0})$	${0.68}_{-0.21}^{+0.28}$	[17,102]	Sy1.5
J0228††	${10}^{-1}\times (3.2_{-1.6}^{+3.1})$	${0.82}_{-0.09}^{+0.16}$	[17,102]	BL,Sy1
POX 52††	${10}^{-1}\times (3.2_{-1.6}^{+3.1})$	${0.56}_{-0.46}^{+0.36}$	[22,102]	Sy1.8

¹ Black hole mass estimated via: optical reverberation mapping^†; $H\alpha$, $H\beta$ or $C\mathtt{IV}$ widths, combined with a subsequent fit of virial scaling relations^††; VLTI GRAVITY interferometry*; an empirical method based on observed correlations between the equivalent width attributed to narrow-line 6.4 Fe K$\alpha$ emission’; and other methods (no symbol).

2.1. Updated Mass–Spin Plane

The mass–spin estimates shown in Table 1 are an updated version of table 1 of the spin review of Ref. [94], incorporating the following changes:

• For the high-mass SMBH H 1821+643, we adopt the spin estimate in Ref. [105] (consistent with the prior bound of Ref. [51]). We note that Ref. [12] argued that the iron K band can be described with a model featuring absorption and distant reflection.
• For the extreme galaxy ESO 033-G002, we quote the mass and spin reported in Ref. [96] – consistent with the spin later estimated by Ref. [124] under a disk reflection spectrum for an extended (ring) coronal geometry.
• For Fairall 9, we consider the spin estimate inferred from spectral modeling of multi-epoch XMM-Newton and Suzaku observations of Ref. [36] without the inclusion of a model component for the soft excess in the Suzaku data (as such an inclusion otherwise drives the spin constraint, as detailed in their discussion). We note that several works have argued that relativistically-broadened Fe K$\alpha$ emission is not required to describe the X-ray spectrum [66] or the X-ray variability [109] of Fairall 9.
• For the Seyfert 1.5 galaxy NGC 4151, we adopt the lower spin bound $a^{*}$$>0.9$ found from an X-ray reflection fit to a joint Swift+Suzaku spectrum which assumed a lamppost coronal geometry [54]. Whilst this geometry seems to be strongly disfavored by joint IXPE, XMM-Newton, and NuSTAR polarimetric and spectroscopic analyses [108,113], a 2023 XRISM observation does reveal relativistically broadened Fe K$\alpha$ emission. A new spin constraint from this XRISM observation is anticipated [119].
• We include 13 low-mass AGN sample spin estimates in Ref. [102], who used a relativistic reflection model to describe the soft excess in XMM-Newton data.
• We do not include the spin constraints for both IRAS 13349+2438 and the high-mass broad-line radio galaxy 4C 74.26, for the reasons outlined in section 6 of Ref. [105].
• We do not consider the spin estimate for NGC 4051 of Ref. [37], as its spin was fixed to the canonical upper limit in their spectral analysis.
• For the canonical type-1 AGN MCG–6-30-15, we conservatively adopt the time-average spin estimate of Ref. [121] ($a^{*}$$>0.65$) from a quasi-simultaneous XRISM, XMM-Newton, and NuSTAR campaign. A revisited spin bound based on time-resolved spectra from this campaign is forthcoming. We note that work prior to the launch of XRISM had inferred tighter spin constraints for this type-1 AGN [15,47]. 
• We update the mass–spin compilation of Ref. [94] with four new SMBHs: Mrk 1044 [71], ESO 033-G002 [96], PG 1426+015 [128], PG 1535+547 [130].

2.2. Interpretation of the Observed Mass–Spin Plane

The large statistical uncertainties of many existing spin estimates make a robust assessment of possible trends challenging. High-mass SMBH spin measurements – where merger-driven spin-down is expected to be most apparent – also remain scarce. Within the full sample of 51 accreting SMBHs and low-mass AGN, only 20 have well-defined upper and lower bounds, while the remaining 31 only have lower limits.

Most existing reflection-based SMBH spin measurements have been obtained on a case-by-case basis, resulting in a heterogeneous dataset with varying reflection-model assumptions and implementations. The majority of the spin estimates in Figure 1 were obtained using variants of the Relxill relativistic X-ray reflection model [44,45,60,99], applied to either broadened Fe K$\alpha$ emission and the Compton hump, or to the soft excess. Close to half of all existing spin estimates (excluding the low-mass sample from Ref. [102]) were based on broadband X-ray spectra covering both the Fe K band and the Compton hump regimes. In only approximately half of these cases (i.e. $\sim 25\%$ of all 51 sources in the full sample), quasi-simultaneous XMM-Newton+NuSTAR observations provide the most comprehensive data: XMM-Newton’s spectral sensitivity is critical to probing the red wing of the Fe K line, while NuSTAR’s high-energy coverage (whose bandpass covers $3-79\mathrm{keV}$) constrains the Compton hump, which is essential for reducing spectral modeling degeneracies.

At present, the disk reflection spectrum of only one accreting SMBH (MCG–06-30-15) has been probed with joint XRISM+XMM-Newton+NuSTAR coverage [121], although similar sensitivity is expected for ongoing and future XRISM targets (including NGC 4151; see Ref. [119]). With the unprecedented spectral resolution of XRISM/Resolve ($\sim 5\mathrm{eV}$), the highest-precision, near-future spin measurements prior to NewAthena are still forthcoming.

Beyond model-dependent systematic uncertainties (which we expand on in Section 3), spin-dependent observational biases must also be considered. For a given accretion rate $\dot{m}$ onto the black hole, high-spin SMBHs (i.e. more luminous SMBHs) are overrepresented in flux-limited samples due to the spin-dependent radiative efficiency $\eta ($$a^{*}$) [33,117]. This effect is suggested in Figure 2, showing that, for a given estimated spin, SMBHs with higher intrinsic X-ray fluxes are more abundant compared to fainter AGN. 

The current observed sample is also heterogeneous in X-ray luminosity, Eddington ratio, spectral type, and redshift. Where available, these quantities are listed in Table 2.

Figure 3 shows no obvious correlation between spin and Eddington ratio for the full sample. This result appears to disfavor models claiming an Eddington-ratio dependent equilibrium spin [102]. However, SMBHs need not be at the equilibrium spin for their Eddington ratio if the Eddington ratio fluctuates on short timescales. Considering the universal equilibrium spin of $a^{*}\approx 0.3$ for luminous magnetized accretion flows proposed by Ref. [123], these data could be explained if most accretion does not proceed in such a highly magnetized fashion.

Future studies using large, homogeneous samples will need to account for the known correlation between the bolometric correction and Eddington fraction (particularly if the Eddington ratio is used to estimate the bolometric luminosity from the $2-10\mathrm{keV}$ luminosity), since neglecting this correlation could bias Eddington ratio estimates [20,64]. We note that most works in the literature adopt bolometric corrections from the observed 5 100Å luminosity. Each of these approaches carries its own caveats: the AGN contribution to $L_{5100}$ is limited by the host-galaxy subtraction method [38], although the 5 00 Å bolometric corrections are generally preferred because they exhibit smaller intrinsic scatter than X-ray bolometric corrections. In parallel, the estimate of 2–10 keV bolometric correction is itself correlated with the Eddington fraction, which – if unaccounted for – can lead to systematically overestimated values of ${\lambda }_{\mathrm{Edd}}$ [23,64]. Figure 4 also shows no obvious correlation between spin and the 2–10 keV luminosity in the sample.

3. Future Prospects: A Decisive Test of Observed Mass–Spin Trends with NewAthena

The current observed SMBH mass–spin sample, while invaluable, remains dominated by lower spin limits and is too heterogeneous to enable decisive tests of SMBH growth scenarios. This limitation has been demonstrated explicitly by Ref. [117], who showed that the current collection of reflection-based spin measurements at the time lacked the statistical power and uniformity required to distinguish between the distinct mass–spin trends predicted for coherent-accretion-dominated versus coherent-accretion+merger-dominated SMBH growth from the Horizon-AGN cosmological simulation. Ref. [117] further showed that strategically sampling the SMBH mass–spin plane with the proposed High-Energy X-ray Probe (HEX-P) [116] – a mission concept with NuSTAR-like high-energy coverage but a substantially larger collecting area – with three mass bins would enable population-level spin measurements. Their approach drew a direct connection to the distinct accretion versus accretion+merger driven growth channels in HorizonAGN by enabling observational tests of their distinct trends in the mass–spin plane, subject to specific requirements in sample size, mass range, and redshift coverage (outlined in section 7 of Ref. [117]).

In addition to sample size limitations, the assessment of systematic uncertainties in spin measurements is equally crucial [76]. These systematics fall broadly into two categories: (i) modeling systematics, arising from both spectral degeneracies and assumptions made by relativistic reflection models, and (ii) instrumental systematics, arising from calibration uncertainties. Recent work has also shown that within the first category, spectral model degeneracies – particularly those involving warm absorbers, ultra-fast outflows, and complex soft X-ray structure – can mimic or obscure relativistically smeared reflection features. Ref. [104] demonstrated this explicitly in the context of NewAthena and also showed that these degeneracies are dramatically reduced when broadband coverage is included to fully probe the Compton hump and characterize the high-energy cutoff. In parallel, a comprehensive analysis that jointly incorporates the impact of different modeling assumptions on the reflection-based spin – such as alternative coronal geometries beyond the lamppost, the use of razor-thin versus razor-thick disk prescriptions, or considering reflected emission within the innermost stable circular orbit – has yet to be completed, although several recent studies have begun to quantify how such choices can affect the recovered spin for a given underlying spin (e.g. Refs. [73,122,124]).

Within this first category, the role of disk density is also increasingly recognized as a key modeling uncertainty. Standard implementations of relxill assume a fixed mid-plane density of $n_{\mathrm{e}}={10}^{15}{\mathrm{cm}}^{-3}$, which directly sets the ionization parameter and is known to be an oversimplification. High-density reflection models relax this assumption by allowing the density to vary, and in several cases alleviate the need for the super-solar iron abundances often inferred with fixed-density models. However, the interplay between density, ionization, and the inner disk metallicity remains poorly understood, and a systematic assessment of how high-density models impact recovered spin values has not yet been performed. In parallel, a further source of uncertainty arises from the poorly constrained inclination distribution of current reflection-based spin measurements: most studies report only approximate inclination values, preventing a proper assessment of correlations between inclination, spin, and other spectral parameters. Very high inferred inclinations can partially mimic the blueshifted wing of the broadened $\mathrm{Fe}\mathrm{K}\alpha$ line, introducing a degeneracy that cannot yet be quantified robustly in the absence of full posterior information for most published analyses.

Within the second category, instrumental calibration remains an important consideration. Ref. [111] demonstrated that machine-learning approaches such as convolutional neural networks (when trained to distinguish astrophysical spectral features from detector-calibration artifacts in synthetic NewAthena spectra) offer a promising pathway towards mitigating these systematics. These developments highlight that progress in SMBH spin studies requires not only larger samples but also improved tools for disentangling physical and instrumental effects. We highlight that careful consideration of systematic uncertainties will be especially critical for NewAthena, whose dramatically reduced Poisson uncertainties – enabled by its much larger collecting area – will shift the limiting factor in reflection-based spin estimates from statistical noise to these systematic effects.

The upcoming NewAthena X-ray observatory is poised to deliver the uniform dataset of reflection-based spin estimates identified as necessary by Ref. [117], while with a mission profile distinct from HEX-P. NewAthena is currently planning a survey of at least 50 nearby SMBHs – beyond the current sample in Figure 1 – that will deliver the first homogeneous, high-precision spin catalog for the local, intermediate-mass AGN population, providing a well-characterized anchor sample for confirming tentative mass–spin predictions. As highlighted by section 7 of Ref. [117], a sample of 50 accreting SMBH may neither overcome the high-spin bias reflected in the current sample, nor uniformly populate the high-mass SMBH end ($M_{\mathrm{BH}}>{10}^9{M}_{\odot }$) in the local universe, where theoretical models of accretion-driven vs. accretion+merger-driven growth differ more significantly. Noting that at $z\sim 0$ only a handful of such massive, X-ray luminous SMBHs exist, the forthcoming NewAthena spin survey of at least 50 nearby AGN will be dominated by SMBHs with intermediate masses. For this reason, the current heterogeneous sample of 51 reflection-based spin estimates will remain essential for spanning the full ${10}^6-{10}^{10}{M}_{\odot }$ mass range required to statistically discriminate between competing mass–spin trends in cosmological models and SAMs. However, we note that many of the existing estimates will need to be revisited – and reobserved with NewAthena if XRISM follow-up is not available at the time of NewAthena’s launch – before such estimates can be used along with NewAthena’s new survey. This is particularly pressing for current spin estimates driven by the reflection interpretation of the soft excess, which has led to high $a^{*}$ estimates in several Narrow-Line Seyfert 1s in the current sample. In such cases, the soft excess itself can act as the dominant driver of the spin constraint: in the absence of a pronounced broadened $\mathrm{Fe}\mathrm{K}\alpha$ line and Compton hump, the forest of relativistically blurred soft X-ray features predicted by reflection models forces the fit toward high spin, effectively yielding lower limits that may not reflect the true underlying spin.

Probing spin evolution across cosmic time will require extending beyond the local sample, since a nearby survey alone cannot map redshift-dependent trends. The value of the NewAthena survey will instead lie in providing a well-characterized anchor sample with unprecedented sensitivity due to its improved collecting area and unprecedented spectral resolution compared to current X-ray missions. We highlight that for distant SMBHs up to $z\sim 1.5$, the rest-frame Fe K band is redshifted into NewAthena’s $0.1-12\mathrm{keV}$ sensitivity window, enabling spin measurements for bright sources at moderate redshift without relying on strong gravitational lensing. This redshift effect opens a complementary pathway for extending spin studies beyond the local universe, although the achievable precision will depend on source brightness and exposure time.

3.1. A Statistical Framework to Probe SMBH Mass–Spin Trends with NewAthena

Hierarchical Bayesian inference offers a particularly powerful and timely tool to extract the underlying spin distribution from both current and future observed mass–spin datasets. This framework has already proven transformative in gravitational-wave astronomy, where it is routinely used by the LVK Collaboration to infer the underlying spin distributions of merging stellar-mass black holes from gravitational-wave signals [92]. Applying analogous techniques to NewAthena’s spin catalog will allow the X-ray community to start addressing if the local SMBH population reflects a mixture of coherent and incoherent accretion, SMBH mergers, and jet-induced spin-down, to quantify the relative importance of these channels at low redshift. These techniques will enable incorporating systematic uncertainties due to spectral model degeneracies, modeling assumptions, and detector calibration, to account for spin-dependent radiative-efficiency selection effects in flux-limited samples, and to enable principled comparisons between physical models of SMBH growth. Such hierarchical population analyses have not yet been attempted for SMBH spins inferred from X-ray reflection, and the first exploratory tests in the context of NewAthena are underway. Preliminary exploration using a small set of hyperparameters – capturing a merger-driven population as a Gaussian about a mean with moderate $a^{*}$ and a truncated power-law function underlying a SMBH population growing primarily via coherent accretion – indicate that this two-component description fails to reproduce the observed mass–spin distribution, illustrating the need for more complex and physically motivated models. The current heterogeneous mass–spin sample of 51 SMBHs – though not yet statistically decisive – provides an ideal laboratory for developing such techniques prior to their application across the NewAthena dataset.

In addition to the spin constraints provided by NewAthena, achieving this goal will require SMBH mass estimates of the highest possible precision, drawing on complementary facilities such as the Nancy Grace Roman Space Telescope to provide robust black hole mass estimates. Moreover, the observational requirements implemented by Ref. [117] for the HEX-P spin survey will need to be revisited in the context of NewAthena, since its spectral capabilities, survey strategy, and redshift reach differ from those assumed in the HEX-P forecasts of Ref. [117]. In particular, unlike HEX-P, NewAthena will not have the high-energy coverage needed to fully characterize the Compton hump or robustly constrain the high-energy cutoff – essential for tight reflection-based spin estimates and to break spectral model degeneracies. Thus, assessing the impact of this limitation and determining how it could affect the distinction between competing mass–spin trends will be a central component of NewAthena’s SMBH spin survey.

Together, NewAthena and hierarchical Bayesian population modeling promise to transform SMBH spin studies in observed SMBH mass–spin distributions. Whilst this combination cannot realistically capture the full SMBH evolution in mass and redshift, it will provide the most robust and controlled benchmark of observed mass–spin trends in the local universe, transforming these observed correlations into a quantitative test of competing growth scenarios.