Mass Scaling Relations Research Articles

The baryon census and the mass-density of stars, neutral gas, and hot gas as a function of halo mass

Abstract We study the stellar, neutral gas content within halos over a halo mass range 1010to1015.5M⊙ and hot X-ray gas content over a halo mass range 1012.8to1015.5M⊙ in the local universe. We combine various empirical datasets of stellar, H i and X-ray observations of galaxies, groups and clusters to establish fundamental baryonic mass vs halo mass scaling relations. These scaling relations are combined with halo mass function to obtain the baryon densities of stars, neutral gas and hot gas (T > 106K), as a function of halo mass. We calculate the contributions of the individual baryonic components to the cosmic baryon fraction. Cosmic stellar mass density ($\Omega _\text{star}=2.09^{+0.21}_{-0.18} \times 10^{-3}$), cosmic H i mass density ($\Omega _\rm{H\,{\small I}}=0.49^{+0.25}_{-0.12} \times 10^{-3}$) and cosmic neutral gas mass density ($\Omega _\text{neutral gas}=0.71^{+0.39}_{-0.18} \times 10^{-3}$) estimates are consistent with previous more direct method measurements of these values, thereby establishing the veracity of our method. We also give an estimate of the cosmic hot plasma density ($\Omega _\text{hot gas}=2.58^{+2.1}_{-0.66} \times 10^{-3}$).

Constraining the Origin of the Nanohertz Gravitational-wave Background by Pulsar Timing Array Observations of Both the Background and Individual Supermassive Binary Black Holes

The gravitational waves (GWs) from supermassive binary black holes (BBHs) have long been sought by pulsar timing array (PTA) experiments, in the forms of both a stochastic GW background (GWB) and individual sources. Evidence for a GWB was reported recently by several PTAs with origins to be determined. Here we use a BBH population synthesis model to investigate the detection probability of individual BBHs by the Chinese PTA (CPTA) and the constraint on the GWB origin that may be obtained by PTA observations of both GWB and individual BBHs. If the detected GWB signal is entirely due to BBHs, a significantly positive redshift evolution (∝ (1 + z)2.07) of the mass scaling relation between supermassive black holes and their host galaxies is required. In this case, we find that the detection probability of individual BBHs is ∼85% or 64% if using a period of 3.4 yr of CPTA observation data, with an expectation of ∼1.9 or 1.0 BBHs detectable with a signal-to-noise ratio ≥3 or 5, and it is expected to increase to >95% if the observation period is extended to 5 yr or longer. Even if the contribution from BBHs to the GWB power signal is as small as ∼10%, a positive detection of individual BBHs can still be expected within an observation period of ∼10 yr. A nondetection of individual BBHs within several years from now jointly with the detected GWB signal can put a strong constraint on the upper limit of the BBH contribution to the GWB signal and help identify/falsify a cosmological origin.

Mass scaling relations for dark halos from an analytic universal outer density profile

Context. The average matter density within the turnaround scale, which demarcates where galaxies shift from clustering around a structure to joining the expansion of the Universe, is an important cosmological probe. However, a measurement of the mass enclosed by the turnaround radius is difficult. Analyses of the turnaround scale in simulated galaxy clusters place the turnaround radius at about three times the virial radius in a ΛCDM universe and at a (present-day) density contrast with the background matter density of the Universe of δ ~ 11. Assessing the mass at such extended distances from a cluster’s center is a challenge for current mass measurement techniques. Consequently, there is a need to develop and validate new mass-scaling relations, to connect observable masses at cluster interiors with masses at greater distances. Aims. Our research aims to establish an analytical framework for the most probable mass profile of galaxy clusters, leading to novel mass scaling relations, allowing us to estimate masses at larger scales. We derive such analytical mass profiles and compare them with those from cosmological simulations. Methods. We used excursion set theory, which provides a statistical framework for the density and local environment of dark matter halos, and complement it with the spherical collapse model to follow the non-linear growth of these halos. Results. The profile we developed analytically showed good agreement (better than 30%, and dependent on halo mass) with the mass profiles of simulated galaxy clusters. Mass scaling relations were obtained from the analytical profile with offset better than 15% from the simulated ones. This level of precision highlights the potential of our model for probing structure formation dynamics at the outskirts of galaxy clusters.

Establishing HI mass vs. stellar mass and halo mass scaling relations using an abundance matching method

Establishing HI mass vs. stellar mass and halo mass scaling relations using an abundance matching method

Effects of boundary conditions on the core-halo mass scaling relation of fuzzy dark matter structures

Effects of boundary conditions on the core-halo mass scaling relation of fuzzy dark matter structures

Size–mass relation of the brightest cluster galaxies at z ∼ 1

ABSTRACT We present the size–mass relation of the brightest cluster galaxies (BCGs) at 0.1 < z < 1.4 using the imaging data obtained by the Hyper Suprime-Cam Subaru Strategic Program. Our sample consists of 471 photometrically selected BCGs with stellar mass logM*/M⊙ = 11–12. We measure the size of the BCGs using i-band imaging and model fits based on a single Sérsic light profile. Stellar masses are determined through spectral energy distribution fitting using Sérsic-modelled photometry data across five optical bands (grizy). The size–mass scaling relation of BCGs is $r_\mathrm{ e}\propto M_*^{0.73-1.00}$ at z < 1, with a slope that does not evolve significantly. The slope of the size–mass relation for BCGs is steeper than other non-BCG galaxies, which implies that BCGs are a special galaxy population. The size of BCGs at a given stellar mass evolves rapidly as ∝ (1 + z)−1.58 ± 0.13 and increases with redshift by a factor of 2.5 from z ∼ 1.2 to z ∼ 0.2. The rapid size growth is in agreement with semi-analytical model results, indicating that the BCG growth is dominated by frequent minor mergers. Furthermore, we explore the size–mass relationship of BCGs with respect to the halo mass of the cluster and find there is no significant correlation, which might imply that a dependence on the environment predominantly affects the outer envelope of the BCGs.

OzDES reverberation mapping program: Stacking analysis with Hβ, Mg ii and C iv

Abstract Reverberation mapping is the leading technique used to measure direct black hole masses outside of the local Universe. Additionally, reverberation measurements calibrate secondary mass-scaling relations used to estimate single-epoch virial black hole masses. The Australian Dark Energy Survey (OzDES) conducted one of the first multi-object reverberation mapping surveys, monitoring 735 AGN up to z ∼ 4, over 6 years. The limited temporal coverage of the OzDES data has hindered recovery of individual measurements for some classes of sources, particularly those with shorter reverberation lags or lags that fall within campaign season gaps. To alleviate this limitation, we perform a stacking analysis of the cross-correlation functions of sources with similar intrinsic properties to recover average composite reverberation lags. This analysis leads to the recovery of average lags in each redshift-luminosity bin across our sample. We present the average lags recovered for the Hβ, Mg ii and C iv samples, as well as multi-line measurements for redshift bins where two lines are accessible. The stacking analysis is consistent with the Radius-Luminosity relations for each line. Our results for the Hβ sample demonstrate that stacking has the potential to improve upon constraints on the R − L relation, which have been derived only from individual source measurements until now.

Merger-driven Growth of Intermediate-mass Black Holes: Constraints from Hubble Space Telescope Imaging of Hyper-luminous X-Ray Sources

Hyper-luminous X-ray sources (HLXs) are extragalactic off-nuclear X-ray sources with luminosities exceeding the theoretical limit for accretion onto stellar-mass compact objects. Many HLXs may represent intermediate-mass black holes (IMBHs) deposited in galaxy halos through mergers, and the properties of the stellar cores surrounding HLXs provide powerful constraints on this scenario. Therefore, we have systematically built the largest sample of HLX candidates with archival Hubble Space Telescope (HST) imaging (24) for the first uniform population study of HLX stellar cores down to low masses. Based on their host galaxy redshifts, at least 21 (88%) have stellar core masses ≥ 107 M ⊙ and hence are consistent with accretion onto massive black holes from external galaxies. In 50% of the sample, the HST imaging reveals features connecting the HLXs with their host galaxies, strongly suggesting against the background/foreground contaminant possibility in these cases. Assuming a mass scaling relation for active galactic nuclei and accounting for an estimated contamination fraction of 29%, up to ∼60% of our sample may be associated with IMBHs. Similar to previously known HLXs, the X-ray luminosities are systematically elevated relative to their stellar core masses, possibly from merger-driven accretion rate enhancements. The least massive stellar cores are preferentially found at larger nuclear offsets and are more likely to remain wandering in their host galaxy halos. The HLX galaxy occupation fraction is ∼ 10−2 and has a strong inverse mass dependence. Up to three of the HLX candidates (12%) are potentially consistent with formation within globular clusters or with exceptionally luminous X-ray binaries.

The hydrostatic-to-lensing mass bias from resolved X-ray and optical-IR data

An accurate reconstruction of galaxy cluster masses is key to use this population of objects as a cosmological probe. In this work we present a study on the hydrostatic-to-lensing mass scaling relation for a sample of 53 clusters whose masses were reconstructed homogeneously in a redshift range between z = 0.05 and 1.07. The M500 mass for each cluster was indeed inferred from the mass profiles extracted from the X-ray and lensing data, without using a priori observable-mass scaling relations. We assessed the systematic dispersion of the masses estimated with our reference analyses with respect to other published mass estimates. Accounting for this systematic scatter does not change our main results, but enables the propagation of the uncertainties related to the mass reconstruction method or used dataset. Our analysis gives a hydrostatic-to-lensing mass bias of (1−b) = 0.739−0.070+0.075 and no evidence of evolution with redshift. These results are robust against possible subsample differences.

Predicting the scaling relations between the dark matter halo mass and observables from generalised profiles I: Kinematic tracers

Abstract We investigate the relationship between a dark matter halo’s mass profile and measures of the velocity dispersion of kinematic tracers within its gravitational potential. By predicting the scaling relation of the halo mass with the aperture velocity dispersion, $M_\mathrm{vir} - \unicode{x03C3}_\mathrm{ap}$ , we present the expected form and dependence of this halo mass tracer on physical parameters within our analytic halo model: parameterised by the halo’s negative inner logarithmic density slope, $\unicode{x03B1}$ , its concentration parameter, c, and its velocity anisotropy parameter, $\unicode{x03B2}$ . For these idealised halos, we obtain a general solution to the Jeans equation, which is projected over the line of sight and averaged within an aperture to form the corresponding aperture velocity dispersion profile. Through dimensional analysis, the $M_\mathrm{vir} - \unicode{x03C3}_\mathrm{ap}$ scaling relation is devised explicitly in terms of analytical bounds for these aperture velocity dispersion profiles: allowing constraints to be placed on this relation for motivated parameter choices. We predict the $M_{200} - \unicode{x03C3}_\mathrm{ap}$ and $M_{500} - \unicode{x03C3}_\mathrm{ap}$ scaling relations, each with an uncertainty of $60.5\%$ and $56.2\%$ , respectively. These halo mass estimates are found to be weakly sensitive to the halo’s concentration and mass scale, and most sensitive to the size of the aperture radius in which the aperture velocity dispersion is measured, the maximum value for the halo’s inner slope, and the minimum and maximum values of the velocity anisotropy. Our results show that a halo’s structural and kinematic profiles impose only a minor uncertainty in estimating its mass. Consequently, spectroscopic surveys aimed at constraining the halo mass using kinematic tracers can focus on characterising other, more complex sources of uncertainty and observational systematics.

First asteroseismic analysis of the globular cluster M80: multiple populations and stellar mass-loss

ABSTRACT Asteroseismology provides a new avenue for accurately measuring the masses of evolved globular cluster (GC) stars. We present the first detections of solar-like oscillations in 47 red giant branch (RGB) and early asymptotic giant branch (EAGB) stars in the metal-poor GC M80; only the second with measured seismic masses. We investigate two areas of stellar evolution and GC science: multiple populations and stellar mass-loss. We detect a distinct bimodality in the EAGB mass distribution. We suggest that this could be due to sub-population membership. If confirmed in future work with spectroscopy, it would be the first direct measurement of a mass difference between sub-populations. A mass difference was not detected between the sub-populations in our RGB sample. We instead measured an average RGB mass of $0.782\pm 0.009~\mathrm{M}_{\odot }$, which we interpret as the average of the sub-populations. Differing mass-loss rates on the RGB have been proposed as the second parameter that could explain the horizontal branch morphology variations between GCs. We calculated an integrated RGB mass-loss separately for each sub-population: $0.12\pm 0.02~\mathrm{M}_{\odot }$ (SP1) and $0.25\pm 0.02~\mathrm{M}_{\odot }$ (SP2). Thus, SP2 stars appear to have enhanced mass-loss on the RGB. Mass-loss is thought to scale with metallicity, which we confirm by comparing our results to a higher metallicity GC, M4. Finally, our study shows the robustness of the Δν-independent mass scaling relation in the low-metallicity (and low surface gravity) regime.

Fundamental scaling relationships revealed in the optical light curves of tidal disruption events

ABSTRACT We present fundamental scaling relationships between properties of the optical/UV light curves of tidal disruption events (TDEs) and the mass of the black hole that disrupted the star. We have uncovered these relations from the late-time emission of TDEs. Using a sample of 63 optically selected TDEs, the latest catalogue to date, we observed flattening of the early-time emission into a near-constant late-time plateau for at least two-thirds of our sources. Compared to other properties of the TDE light curves (e.g. peak luminosity or decay rate) the plateau luminosity shows the tightest correlation with the total mass of host galaxy (p-value of 2 × 10−6, with a residual scatter of 0.3 dex). Physically this plateau stems from the presence of an accretion flow. We demonstrate theoretically and numerically that the amplitude of this plateau emission is strongly correlated with black hole mass. By simulating a large population (N = 106) of TDEs, we determine a plateau luminosity-black hole mass scaling relationship well described by $\log _{10} \left({{M_{\bullet }}/M_\odot }\right) = 1.50 \log _{10} \left({ L_{\rm plat}}/10^{43} \, {\rm erg\, s^{-1}}\right) + 9.0$ (here Lplat is measured at 6 × 1014 Hz in the rest frame). The observed plateau luminosities of TDEs and black hole masses in our large sample are in excellent agreement with this simulation. Using the black hole mass predicted from the observed TDE plateau luminosity, we reproduce the well-known scaling relations between black hole mass and galaxy velocity dispersion. The large black hole masses of 10 of the TDEs in our sample allow us to provide constraints on their black hole spins, favouring rapidly rotating black holes. Finally, we also discover two significant correlations between early time properties of optical TDE light curves (the g-band peak luminosity and radiated energy) and the TDEs black hole mass.

Resolved Kennicutt–Schmidt law in two strongly lensed star-forming galaxies at redshift 1

We study the star formation rate (SFR) vs. molecular gas mass (Mmol) scaling relation from hundreds to thousands of parsec in two strongly lensed galaxies at redshift z ∼ 1, the Cosmic Snake and A521. We trace the SFR using extinction-corrected rest-frame UV observations with the Hubble Space Telescope (HST), and Mmol using detections of the CO(4–3) line with the Atacama Large Millimeter/submillimeter Array (ALMA). The similar angular resolutions of our HST and ALMA observations of 0.15 − 0.2″ combined with magnifications reaching μ > 20 enable us to resolve structures in the galaxies of sizes lower than 100 pc. These resolutions are close to those of studies of nearby galaxies. This allows us to investigate for the first time the Kennicutt–Schmidt (KS) law (SFR–Mmol surface densities) at different spatial scales, from galactic scales to ∼100 pc scales, in galaxies at z ∼ 1. At integrated scales we find that both galaxies satisfy the KS law defined by galaxies at redshifts between 1 and 2.5. We test the resolved KS (rKS) law in cells of sizes down to 200 pc in the two galaxies. We observe that this relationship generally holds in these z ∼ 1 galaxies, although its scatter increases significantly with decreasing spatial scales. We check the scale dependence of the spatial correlation between the surface densities of SFR and Mmol by focusing on apertures centred on individual star-forming regions and molecular clouds. We conclude that star-forming regions and molecular clouds become spatially de-correlated at ≲1 kpc in the Cosmic Snake, whereas they appear de-correlated at all spatial scales (from 400 pc to 6 kpc) in A521.

WALLABY pre-pilot survey: ultra-diffuse galaxies in the Eridanus supergroup

ABSTRACT We present a pilot study of the atomic neutral hydrogen gas (H i) content of ultra-diffuse galaxy (UDG) candidates. In this paper, we use the pre-pilot Eridanus field data from the Widefield ASKAP L-band Legacy All-sky Blind Survey to search for H i in UDG candidates found in the Systematically Measuring Ultra-diffuse Galaxies survey (SMUDGes). We narrow down to 78 SMUDGes UDG candidates within the maximum radial extents of the Eridanus subgroups for this study. Most SMUDGes UDGs candidates in this study have effective radii smaller than 1.5 kpc and thus fail to meet the defining size threshold. We only find one H i detection, which we classify as a low-surface-brightness dwarf. Six putative UDGs are H i-free. We show the overall distribution of SMUDGes UDG candidates on the size–luminosity relation and compare them with low-mass dwarfs on the atomic gas fraction versus stellar mass scaling relation. There is no correlation between gas-richness and colour indicating that colour is not the sole parameter determining their H i content. The evolutionary paths that drive galaxy morphological changes and UDG formation channels are likely the additional factors to affect the H i content of putative UDGs. The actual numbers of UDGs for the Eridanus and NGC 1332 subgroups are consistent with the predicted abundance of UDGs and the halo virial mass relation, except for the NGC 1407 subgroup, which has a smaller number of UDGs than the predicted number. Different group environments suggest that these putative UDGs are likely formed via the satellite accretion scenario.

Supermassive black holes in a mass-limited galaxy sample

ABSTRACT The observed scaling relations between supermassive black hole masses and their host galaxy properties indicate that supermassive black holes influence the evolution of galaxies. However, the scaling relations may be affected by selection biases. We propose to measure black hole masses in a mass-limited galaxy sample including all non-detections to inprove constraints on galaxy mass – black hole mass scaling relations and test for selection bias. We use high-spatial resolution spectroscopy from the Keck and Gemini telescopes, and the Jeans Anisotropic Modelling method to measure black hole masses in early-type galaxies from the Virgo Cluster. We present four new black hole masses and one upper limit in our mass-selected sample of galaxies of galaxy mass (1.0–3.2) $\times 10^{10} \, \mathrm{M}_\odot$. This brings the total measured to 11 galaxies out of a full sample of 18 galaxies, allowing us to constrain scaling relations. We calculate a lower limit for the average black hole mass in our sample of $3.7 \times 10^{7} \, \mathrm{M}_\odot$. This is at an average galaxy stellar mass of $(1.81 \pm 0.14)\times 10^{10} \, \mathrm{M}_\odot$ and an average bulge mass of $(1.31 \pm 0.15) \times 10^{10} \, \mathrm{M}_\odot$. This lower limit shows that black hole masses in early-type galaxies are not strongly affected by selection biases.

Interpreting Sunyaev–Zel’dovich observations with MillenniumTNG: mass and environment scaling relations

ABSTRACT Sunyaev–Zel’dovich (SZ) measurements can dramatically improve our understanding of the intergalactic medium and the role of feedback processes in galaxy formation, allowing us to calibrate important astrophysical systematics in cosmological constraints from weak lensing galaxy clustering surveys. However, the signal is only measured in a two-dimensional projection, and its correct interpretation relies on understanding the connection between observable quantities and the underlying intrinsic properties of the gas, in addition to the relation between the gas and the underlying matter distribution. One way to address these challenges is through the use of hydrodynamical simulations such as the high-resolution, large-volume MillenniumTNG suite. We find that measurements of the optical depth, τ, and the Compton-y parameter, Y, receive large line-of-sight contributions that can be removed effectively by applying a compensated aperture photometry filter. In contrast with other τ probes (e.g. X-rays and fast radio bursts), the kinematic SZ-inferred τ receives most of its signal from a confined cylindrical region around the halo due to the velocity decorrelation along the line of sight. Additionally, we perform fits to the Y–M and τ–M scaling relations and report best-fitting parameters adopting the smoothly broken power law formalism. We note that subgrid physics modelling can broaden the error bar on these by 30 per cent for intermediate-mass haloes (${\sim }10^{13} \, {\rm M}_{\odot }$). The scatter of the scaling relations can be captured by an intrinsic dependence on concentration and an extrinsic dependence on tidal shear. Finally, we comment on the effect of using galaxies rather than haloes in observations, which can bias the inferred profiles by ∼20 per cent for L* galaxies.

The impact of black hole scaling relation assumptions on the mass density of black holes

ABSTRACT We examine the effect of supermassive black hole (SMBH) mass scaling relation choice on the inferred SMBH mass population since redshift z ∼ 3. To make robust predictions for the gravitational wave background (GWB), we must have a solid understanding of the underlying SMBH demographics. Using the SDSS and 3D-HST + CANDELS surveys for 0 < z < 3, we evaluate the inferred SMBH masses from two SMBH–galaxy scaling relations: MBH–Mbulge and MBH–σ. Our SMBH mass functions come directly from stellar mass measurements for MBH–Mbulge, and indirectly from stellar mass and galaxy radius measurements along with the galaxy mass fundamental plane for MBH–σ. We find that there is a substantial difference in predictions especially for z > 1, and this difference increases out to z = 3. In particular, we find that using velocity dispersion predicts a greater number of SMBHs with masses greater than 109 M⊙. The GWB that pulsar timing arrays find evidence for is higher in amplitude than expected from GWB predictions which rely on high-redshift extrapolations of local SMBH mass–galaxy scaling relations. The difference in SMBH demographics resulting from different scaling relations may be the origin for the mismatch between the signal amplitude and predictions. Generally, our results suggest that a deeper understanding of the potential redshift evolution of these relations is needed if we are to draw significant insight from their predictions at z > 1.

Testing the Linear Relationship between Black Hole Mass and Variability Timescale in Low-luminosity AGNs at Submillimeter Wavelengths

The variability of submillimeter emission provides a useful tool to probe the accretion physics in low-luminosity active galactic nuclei. We accumulate four years of observations using the Submillimeter Array for Centaurus A, NGC 4374, NGC 4278, and NGC 5077, and one year of observations for NGC 4552 and NGC 4579. All sources are variable. We measure the characteristic timescale at which the variability is saturated by modeling these sources’ light curves as a damped random walk. We detect a timescale for all the sources except NGC 4552. The detected timescales are comparable to the orbital timescale at the event horizon scale for most sources. Combined with previous studies, we show a correlation between the timescale and the black hole mass over 3 orders of magnitude. This discovery suggests the submillimeter emission is optically thin with the emission originating from the event horizon. The mass scaling relationship further suggests that a group of radio sources with a broadband spectrum that peaks at submillimeter wavelengths have similar inner accretion physics. Sources that follow this relationship may be good targets for high-resolution imaging with the Event Horizon Telescope.

Measuring the X-ray luminosities of DESI groups from eROSITA Final Equatorial-Depth Survey – I. X-ray luminosity–halo mass scaling relation

ABSTRACT We use the eROSITA Final Equatorial-Depth Survey (eFEDS) to measure the rest-frame 0.1–2.4 keV band X-ray luminosities of ∼600 000 DESI groups using two different algorithms in the overlap region of the two observations. These groups span a large redshift range of 0.0 ≤ zg ≤ 1.0 and group mass range of $10^{10.76}\, h^{-1}\, \mathrm{M}_{\odot } \le M_h \le 10^{15.0}\, h^{-1}\, \mathrm{M}_{\odot }$. (1) Using the blind detection pipeline of eFEDS, we find that 10932 X-ray emission peaks can be cross-matched with our groups, ∼38 per cent of which have a signal-to-noise ratio $\rm {S}/\rm {N} \ge 3$ in X-ray detection. Comparing to the numbers reported in previous studies, this matched sample size is a factor of ∼6 larger. (2) By stacking X-ray maps around groups with similar masses and redshifts, we measure the average X-ray luminosity of groups as a function of halo mass in five redshift bins. We find that in a wide halo mass range, the X-ray luminosity, LX, is roughly linearly proportional to Mh and quite independent to the redshift of the groups. (3) We use a Poisson distribution to model the X-ray luminosities obtained using two different algorithms and obtain the best-fit $L_{\rm X}=10^{28.46\pm 0.03}M_{\rm h}^{1.024\pm 0.002}$ and $L_{\rm X}=10^{26.73 \pm 0.04}M_{\rm h}^{1.140 \pm 0.003}$ scaling relations, respectively. The best-fit slopes are flatter than the results previously obtained but closer to a self-similar prediction.

Scaling relations of X-ray luminous clusters in the Hyper Suprime-Cam Subaru Strategic Program field

ABSTRACT We present the XMM–Newton X-ray analysis of 19 X-ray luminous galaxy clusters of low- to mid-redshift (<0.4) selected from the MCXC (Meta-Catalog of X-Ray Detected Clusters of Galaxies) cluster catalogue in the Hyper Suprime-Cam Subaru Strategic Programme field. We derive the hydrostatic equilibrium mass and study scaling relations using (i) the whole sample, (ii) only relaxed clusters, and (iii) only disturbed clusters. When considering the whole sample, the YX–Mtot and Mgas–Mtot relations agree with self-similarity. In terms of morphology, relaxed clusters show a flatter relation in LX,ce–Mtot, LX,bol–Mtot, LX,ce–T, Lbol,ce–T, Mgas–Mtot, and YX–Mtot. The Lbol,ce–Mtot, LX,ce–Mtot Lbol,ce–T, and LX,ce–T relations show a slope ∼3σ steeper. The residuals in the Mgas–Mtot and T–Mtot relations and the intrinsic covariance between Mgas and T show hints of positive correlation, casting doubt on whether the YX parameter is a truly low-scatter mass proxy. The Mgas–Mtot and T–Mtot plots colour coded with the offset of the LX,ce–Mtot relation show these two relations to be brightness dependent but not the LX,ce–T relation, suggesting that relations involving Mtot are biased due to sample selection based on luminosity. Following the work that studied an optical sample and combining our result with literature studies, we find that Mtot derived not using mass proxies deviates from LX ∝ $M_{\rm gas}^{2}M_{\rm tot}^{-1}$ and Mtot based on hydrostatic equilibrium is more massive than what is expected by their relation using caustic masses. This indicates that mass bias plays an important role in scaling relations.