Mass-temperature Relation Research Articles

Gaia BH1: A Key for Understanding the Demography of Low-q Binaries in the Milky Way Galaxy

The recently discovered Gaia BH1 binary system, a Sun-like star and a dark object (presumably a black hole), may significantly change our understanding of the population of binaries. The paper presents the components mass ratio (q) distributions of binary systems of different observational classes. They all show a significant shortage of low-q systems. In this work, I demonstrate (quantitatively) how our ignorance extends, and point out the importance of discovering and studying systems like Gaia BH1. In addition, an approximate mass–temperature relation and mass ratio–magnitude difference relation for main-sequence stars are presented here.

The Mass–Temperature Relation for B and Early A Stars Based on International Ultraviolet Explorer Spectra of Detached Eclipsing Binaries

Ultraviolet spectra were taken of 25 detached eclipsing binaries (DEBs) with spectral types O, B, and early A with the International Ultraviolet Explorer satellite in the 1150–1900 Å region. The spectra were compared with BOSZ model atmospheres. The composite spectra of the DEBs were modeled by a combination of models representing the hot and cool components, and the temperatures of the hottest components of the systems were determined. From these temperatures a direct mass–temperature relation was obtained for stars close to the main sequence with solar metallicity for B and early A stars: log M/M ⊙ = −5.90 ± 0.27 + (1.56 ± 0.07) × log T. This relation allows a mass to be inferred for comparable stars from an ultraviolet spectrum. The five chemically peculiar Am stars in the sample have larger radii than normal A stars of the same mass.

The Halo Mass–Temperature Relation for Clusters, Groups, and Galaxies

The halo mass–temperature (M–T) relation for a sample of 216 galaxy clusters, groups, and individual galaxies observed by the Chandra X-ray Observatory is presented. Using accurate spectral measurements of their hot atmospheres, we derive the M–T relation for systems with temperatures ranging between 0.4 and 15.0 keV. We measure the total masses of the clusters, groups, and galaxies at radius R 2500, finding that the M 2500 ∝ T α relation follows a power law with α = 1.65 ± 0.06. Our relation agrees with recent lensing studies of the M–T relation at R 200 and is consistent with self-similar theoretical predictions and recent simulations. This agreement indicates that the M–T relation is weakly affected by nongravitational heating processes. Using lensing masses within R 200 we find M 200–T follows a power law with a slope of 1.61 ± 0.19, consistent with the M 2500–T relation. No evidence for a break or slope change is found in either relation. Potential biases associated with sample selection, evolution, and the assumption of hydrostatic equilibrium that may affect the scaling are examined. No significant impacts attributable to these biases are found. Non-cool-core clusters and early spirals produce higher scatter in the M–T relation than cool-core clusters and elliptical galaxies.

EROSITA spectro-imaging analysis of the Abell 3408 galaxy cluster

Context.The X-ray telescope eROSITA on board the newly launched Spectrum-Roentgen-Gamma (SRG) mission serendipitously observed the galaxy cluster Abell 3408 (A3408) during the performance verification observation of the active galactic nucleus 1H 0707–495. The field of view of eROSITA is one degree, which allowed us to trace the intriguing elongated morphology of the nearby (z= 0.0420) A3408 cluster. Despite its brightness (F500≈ 7 × 10−12ergs s−1cm−2) and large extent (r200≈ 21'), it has not been observed by any modern X-ray observatory in over 20 yr. A neighboring cluster in the NW direction, A3407 (r200≈ 18',z= 0.0428), appears to be close at least in projection (~1.7 Mpc). This cluster pair might be in a pre- or post-merger state.Aims.We aim to determine the detailed thermodynamical properties of this special cluster system for the first time. Furthermore, we aim to determine which of the previously suggested merger scenarios (pre- or post-merger) is preferred.Methods.We performed a detailed X-ray spectro-imaging analysis of A3408. We constructed particle-background-subtracted and exposure-corrected images and surface brightness profiles in different sectors. The spectral analysis was performed out to 1.4r500and included normalization, temperature, and metallicity profiles determined from elliptical annuli aligned with the elongation of A3408. Additionally, a temperature map is presented that depicts the distribution of the intracluster medium (ICM) temperature. Furthermore, we make use of data from the ROSAT all-sky survey to estimate some bulk properties of A3408 and A3407, using the growth-curve analysis method and scaling relations.Results.The imaging analysis shows the complex morphology of A3408 with a strong elongation in the SE-NW direction. This is quantified by comparing the surface brightness profiles of the NW, SW, SE, and NE directions, where the NW and SE directions show a significantly higher surface brightness than the other directions. We determine a gas temperaturekBr500= (2.23 ± 0.09) keV in the range 0.2r500to 0.5r500from the spectral analysis. The temperature profile reveals a hot core within two arcminutes of the emission peak, ${k_{\rm{B}}}T = 3.04_{- 0.25}^{+ 0.29}$ keV. Employing a mass–temperature relation, we obtainM500= (9.27 ± 0.75) × 1013M⊙iteratively. Ther200of A3407 and A3408 are found to overlap in projection, which makes ongoing interactions plausible. The two-dimensional temperature map reveals higher temperatures in the W than in the E direction.Conclusions.The elliptical morphology together with the temperature distribution suggests that A3408 is an unrelaxed system. The system A3407 and A3408 is likely in a pre-merger state, with some interactions already affecting the ICM thermodynamical properties. In particular, increased temperatures in the direction of A3407 indicate adiabatic compression or shocks due to the starting interaction.

Low X-ray surface brightness clusters: implications on the scatter of the M–T and L–T relations

ABSTRACT We aim at studying scaling relations of a small but well-defined sample of galaxy clusters that includes the recently discovered class of objects that are X-ray faint for their mass. These clusters have an average low X-ray surface brightness, a low gas fraction, and are underrepresented (by a factor of 10) in X-ray surveys or entirely absent in Sunyaev-Zeldovich (SZ) surveys. With the inclusion of these objects, we find that the temperature–mass relation has an unprecedentedly large scatter, 0.20 ± 0.03 dex at fixed mass, as wide as allowed by the temperature range, and the location of a cluster in this plane depends on its surface brightness. Clusters obey a relatively tight luminosity–temperature relation independently of their brightness. We interpret the wide difference in scatter around the two relations as due to the fact that X-ray luminosity and temperature are dominated by photons coming from small radii (in particular for T we used a 300 kpc aperture radius) and strongly affected by gas thermodynamics (e.g. shocks and cool cores), whereas mass is dominated by dark matter at large radii. We measure a slope of 2.0 ± 0.2 for the L500–T relation. Given the characteristics of our sample, this value is free from collinearity (degeneracy) between evolution and slope and from hypothesis on the undetected population, which both affect the analysis of X-ray-selected samples, and can therefore be profitably used both as reference and to break the aforementioned degeneracy of X-ray-selected samples.

Super interacting dark sector: An improvement on self-interacting dark matter via scaling relations of galaxy clusters

Self-interacting dark matter is known as one of the most appropriate candidates for dark matter. Due to its excellent success in removing many astrophysical problems, particularly in small scale structure, studying this model has taken on added significance. In this paper, we focus on the results of two previously performed simulations of cluster sized halos with self-interacting dark matter and introduce a new function for the density profile of galaxy clusters, which can perfectly describe the result of these simulations. This density profile helps to find a velocity dispersion profile and also a relation between cluster mass and concentration parameter. Using these relations, we investigate two scaling relations of galaxy clusters, namely mass-velocity dispersion and mass-temperature relations. The scaling relations reveal that in the self-interacting dark matter model, halos are more massive than what the standard non-interacting model predicts for any fixed temperature. We also study the mass-temperature relation for a hybrid interacting model, which is a combination of self-interacting dark matter idea with another model of the dark sector in which dark matter particle mass is determined according to its interaction with dark energy. This super interacting dark sector (SIDS) model can change the mass-temperature relation to a modified form that has the same result as a non-interacting model. Finally, we provide quantitative expressions which can describe the constants of this interacting model with the value of cross-section per unit mass of dark matter particles.

Effect of interacting dark energy on mass-temperature relation in galaxy clusters

There are a variety of cosmological models for dark matter and dark energy in which a possible interaction is considered between these two significant components of the universe. We focus on five suggested models of interacting dark matter and dark energy and derive the modified virial theorem for them by developing a previous approach. It provides an opportunity to study the evolution of this modified virial theorem with time and interacting constants for different interacting models. Then we use this obtained virial condition to investigate the modified mass-temperature relation in galaxy clusters via three various methods. It reveals that the effect of interaction between dark matter and dark energy merely appears in the normalization factor of $M\propto T^{\frac{3}{2}}$. This relation also leads to a new constraint on the constants of interacting models, which only depends on the concentration parameter and density profile of the cluster. Then we use five observational data sets to check some proposed figures for the constants of interaction which have been resulted from other observational constraints. Finally, by fitting the observational results to the modified mass-temperature relation, we obtain values for interacting constants of three models and four specific cases of the two remained models. In agreement with many other observational outcomes, we find that according to observational data for masses and temperatures of the galaxy clusters, energy transfer occurs from dark matter to dark energy in the seven investigated models.

Effect of the new extended uncertainty principle on black hole thermodynamics

In this paper we study the thermodynamic properties of the Schwarzschild black hole using a new form of the extended uncertainty principle. By calculating the corrected mass-temperature relation, we investigate the limit of lower bound for the extended-uncertainty-principle–corrected black hole temperature. Also, we obtain the extended-uncertainty-principle–corrected entropy and heat capacity. We compare the behaviors of the usual form and the corrected form of thermodynamic properties for the static black hole.

The XXL Survey

Context.Scaling relations between cluster properties embody the formation and evolution of cosmic structure. Intrinsic scatters and correlations between X-ray properties are determined from merger history, baryonic processes, and dynamical state.Aims.We look for an unbiased measurement of the scatter covariance matrix among the three main X-ray observable quantities attainable in large X-ray surveys: temperature, luminosity, and gas mass. This also gives us the cluster property with the lowest conditional intrinsic scatter at fixed mass.Methods.Intrinsic scatters and correlations can be measured under the assumption that the observable properties of the intra-cluster medium hosted in clusters are log-normally distributed around power-law scaling relations. The proposed method is self-consistent, based on minimal assumptions, and requires neither external calibration by weak lensing, or dynamical or hydrostatic masses, nor the knowledge of the mass completeness.Results.We analysed the 100 brightest clusters detected in the XXL Survey and their X-ray properties measured within a fixed radius of 300 kpc. The gas mass is the less scattered proxy (∼8%). The temperature (∼20%) is intrinsically less scattered than the luminosity (∼30%), but it is measured with a larger observational uncertainty. We found some evidence that gas mass, temperature, and luminosity are positively correlated. Time evolutions are in agreement with the self-similar scenario, but the luminosity–temperature and the gas mass–temperature relations are steeper.Conclusion.Positive correlations between X-ray properties can be determined by the dynamical state and the merger history of the halos. The slopes of the scaling relations are affected by radiative processes.

Mass-temperature relation in ΛCDM and modified gravity

We derive the mass-temperature relation using an improved top-hat model and a continuous formation model which takes into account the effects of the ordered angular momentum acquired through tidal-torque interaction between clusters, random angular momentum, dynamical friction, and modifications of the virial theorem to include an external pressure term usually neglected. We show that the mass-temperature relation differs from the classical self-similar behavior, $M \propto T^{3/2}$, and shows a break at $3--4$ keV, and a steepening with a decreasing cluster temperature. We then compare our mass-temperature relation with those obtained in the literature with $N$-body simulations for $f(R)$ and symmetron models. We find that the mass-temperature relation is not a good probe to test gravity theories beyond Einstein's general relativity, because the mass-temperature relation of the $\Lambda$CDM model is similar to that of the modified gravity theories.

Black hole temperature and Unruh effect from the extended uncertainty principle

In this paper, we investigate the thermodynamic properties of the Schwarzschild black hole and modified Unruh effect by using the simplest form of the extended uncertainty principle (EUP). We obtain the mass-temperature relation and find that there should exist the lower bound for the EUP black hole temperature. Besides, we discuss the modified Unruh effect for EUP. We find that the modified Unruh temperature is larger than the Unruh temperature.

Halo Concentrations and the Fundamental Plane of Galaxy Clusters

According to the standard cold dark matter (CDM) cosmology, the structure of dark halos including those of galaxy clusters reflects their mass accretion history. Older clusters tend to be more concentrated than younger clusters. Their structure, represented by the characteristic radius r s and mass M s of the Navarro–Frenk–White (NFW) density profile, is related to their formation time. In this study, we showed that r s , M s , and the X-ray temperature of the intracluster medium (ICM), T X , form a thin plane in the space of ( log r s , log M s , log T X ) . This tight correlation indicates that the ICM temperature is also determined by the formation time of individual clusters. Numerical simulations showed that clusters move along the fundamental plane as they evolve. The plane and the cluster evolution within the plane could be explained by a similarity solution of structure formation of the universe. The angle of the plane shows that clusters have not achieved “virial equilibrium” in the sense that mass/size growth and pressure at the boundaries cannot be ignored. The distribution of clusters on the plane was related to the intrinsic scatter in the halo concentration–mass relation, which originated from the variety of cluster ages. The well-known mass–temperature relation of clusters ( M Δ ∝ T X 3 / 2 ) can be explained by the fundamental plane and the mass dependence of the halo concentration without the assumption of virial equilibrium. The fundamental plane could also be used for calibration of cluster masses.

Mass-transfer properties of overcontact systems in the Kepler eclipsing binary catalog

Abstract We selected mass-transferring binary candidates from the catalog of Kepler eclipsing binary stars and investigated the dependence of the mass-transfer rate on several astrophysical quantities, including orbital period, semi-major axis, mass ratio, fill-out factor, temperature, and mass. We selected the candidates using O − C diagrams and calculated their mass-transfer rates. Primary masses were obtained from the mass–temperature relation, and the temperatures of the component stars were extracted from a catalog of temperatures for Kepler eclipsing binary stars. The mass-transfer rates of overcontact systems have associations with astrophysical quantities that seem to differ from those of semi-detached or detached systems. These associations indicate that mass exchange from more- to less-massive components (less- to more-massive components) generally becomes rapid (slow) as the mass exchange evolves. However, for mass exchange from more- to less-massive components, this tendency is not reasonable for binaries with a short period (P < 0.4 d) and low mass (M1 < 1.2 M⊙) because the correlations of these binaries are opposite to those of binaries with a long period and high mass. These different correlations likely arise from differences in correlation between subtypes of W UMa systems (i.e., W- and A-types). Alternatively, when mass exchange from more- to less-massive components reoccurs after a mass-ratio reversal, its properties may differ from those of the first mass exchange.

A New Interpretation of the Mass–Temperature Relation and Mass Calibration of Galaxy Clusters Based on the Fundamental Plane

Abstract Observations and numerical simulations have shown that the relation between the mass scaled with the critical density of the universe and the X-ray temperature of galaxy clusters is approximately represented by M Δ ∝ T X 3 / 2 (e.g., Δ = 500 ). This relation is often interpreted as evidence that clusters are in virial equilibrium. However, the recently discovered fundamental plane (FP) of clusters indicates that the temperature of clusters primarily depends on a combination of the characteristic mass M s and radius r s of the Navarro–Frenk–White profile rather than M Δ. Moreover, the angle of the FP revealed that clusters are not in virial equilibrium because of continuous mass accretion from the surrounding matter. By considering both the FP and the mass dependence of the cluster concentration parameter, we show that this paradox can be solved and the relation M Δ ∝ T X 3 / 2 actually reflects the central structure of clusters. We also find that the intrinsic scatter in the halo concentration–mass relation can largely account for the spread of clusters on the FP. We also show that X-ray data alone form the FP and the angle and the position are consistent with those of the FP constructed from gravitational lensing data. We demonstrate that a possible shift between the two FPs can be used to calibrate cluster masses obtained via X-ray observations.

Black Hole Thermodynamics and Generalized Uncertainty Principle with Higher Order Terms in Momentum Uncertainty

We study the modification of thermodynamic properties of Schwarzschild and Reissner-Nordström black hole in the framework of generalized uncertainty principle with correction terms up to fourth order in momentum uncertainty. The mass-temperature relation and the heat capacity for these black holes have been investigated. These have been used to obtain the critical and remnant masses. The entropy expression using this generalized uncertainty principle reveals the area law up to leading order logarithmic corrections and subleading corrections of the form 1/An. The mass output and radiation rate using Stefan-Boltzmann law have been computed which show deviations from the standard case and the case with the simplest form for the generalized uncertainty principle.

The cosmological analysis of X-ray cluster surveys

Context. This paper is the fourth of a series evaluating the ASpiX cosmological method, based on X-ray diagrams, which are constructed from simple cluster observable quantities, namely: count rate (CR), hardness ratio (HR), core radius (rc), and redshift. Aims. Following extensive tests on analytical toy catalogues (Paper III), we present the results of a more realistic study over a 711 deg2 template-based maps derived from a cosmological simulation. Methods. Dark matter haloes from the Aardvark simulation have been ascribed luminosities, temperatures, and core radii, using local scaling relations and assuming self-similar evolution. The predicted X-ray sky-maps were converted into XMM event lists, using a detailed instrumental simulator. The XXL pipeline runs on the resulting sky images, produces an observed cluster catalogue over which the tests have been performed. This allowed us to investigate the relative power of various combinations of the CR, HR, rc, and redshift information. Two fitting methods were used: a traditional Markov chain Monte Carlo (MCMC) approach and a simple minimisation procedure (Amoeba) whose mean uncertainties are a posteriori evaluated by means of synthetic catalogues. The results were analysed and compared to the predictions from the Fisher analysis (FA). Results. For this particular catalogue realisation, assuming that the scaling relations are perfectly known, the CR-HR combination gives σ8 and Ωm at the 10% level, while CR-HR-rc-z improves this to ≤3%. Adding a second HR improves the results from the CR-HR1-rc combination, but to a lesser extent than when adding the redshift information. When all coefficients of the mass-temperature relation (M-T, including scatter) are also fitted, the cosmological parameters are constrained to within 5–10% and larger for the M-T coefficients (up to a factor of two for the scatter). The errors returned by the MCMC, those by Amoeba and the FA predictions are in most cases in excellent agreement and always within a factor of two. We also study the impact of the scatter of the mass-size relation (M-Rc) on the number of detected clusters: for the cluster typical sizes usually assumed, the larger the scatter, the lower the number of detected objects. Conclusions. The present study confirms and extends the trends outlined in our previous analyses, namely the power of X-ray observable diagrams to successfully and easily fit at the same time, the cosmological parameters, cluster physics, and the survey selection, by involving all detected clusters. The accuracy levels quoted should not be considered as definitive. A number of simplifying hypotheses were made for the testing purpose, but this should affect any method in the same way. The next publication will consider in greater detail the impact of cluster shapes (selection and measurements) and of cluster physics on the final error budget by means of hydrodynamical simulations.

Cosmological hydrodynamical simulations of galaxy clusters: X-ray scaling relations and their evolution

We analyse cosmological hydrodynamical simulations of galaxy clusters to study the X-ray scaling relations between total masses and observable quantities such as X-ray luminosity, gas mass, X-ray temperature, and $Y_{X}$. Three sets of simulations are performed with an improved version of the smoothed particle hydrodynamics GADGET-3 code. These consider the following: non-radiative gas, star formation and stellar feedback, and the addition of feedback by active galactic nuclei (AGN). We select clusters with $M_{500} > 10^{14} M_{\odot} E(z)^{-1}$, mimicking the typical selection of Sunyaev-Zeldovich samples. This permits to have a mass range large enough to enable robust fitting of the relations even at $z \sim 2$. The results of the analysis show a general agreement with observations. The values of the slope of the mass-gas mass and mass-temperature relations at $z=2$ are 10 per cent lower with respect to $z=0$ due to the applied mass selection, in the former case, and to the effect of early merger in the latter. We investigate the impact of the slope variation on the study of the evolution of the normalization. We conclude that cosmological studies through scaling relations should be limited to the redshift range $z=0-1$, where we find that the slope, the scatter, and the covariance matrix of the relations are stable. The scaling between mass and $Y_X$ is confirmed to be the most robust relation, being almost independent of the gas physics. At higher redshifts, the scaling relations are sensitive to the inclusion of AGNs which influences low-mass systems. The detailed study of these objects will be crucial to evaluate the AGN effect on the ICM.

Probing modified gravity via the mass-temperature relation of galaxy clusters

We propose that the mass-temperature relation of galaxy clusters is a prime candidate for testing gravity theories beyond Einstein's general relativity, for modified gravity models with universal coupling between matter and the scalar field. For non-universally coupled models we discover that the impact of modified gravity can remain hidden from the mass-temperature relation. Using cosmological simulations, we find that in modified gravity the mass-temperature relation varies significantly from the standard gravity prediction of $M \propto T^{1.73}$. To be specific, for symmetron models with a coupling factor of $\beta=1$ we find a lower limit to the power law as $M\propto T^{1.6}$; and for f(R) gravity we compute predictions based on the model parameters. We show that the mass-temperature relation, for screened modified gravities, is significantly different from that of standard gravity for the less massive and colder galaxy clusters, while being indistinguishable from Einstein's gravity at massive, hot galaxy clusters. We further investigate the mass-temperature relation for other mass estimates than the thermal mass estimate, and discover that the gas mass-temperature results show an even more significant deviations from Einstein's gravity than the thermal mass-temperature.

The scatter and evolution of the global hot gas properties of simulated galaxy cluster populations

We use the cosmo-OWLS suite of cosmological hydrodynamical simulations to investigate the scatter and evolution of the global hot gas properties of large simulated populations of galaxy groups and clusters. Our aim is to compare the predictions of different physical models and to explore the extent to which commonly-adopted assumptions in observational analyses (e.g. self-similar evolution) are violated. We examine the relations between (true) halo mass and the X-ray temperature, X-ray luminosity, gas mass, Sunyaev-Zel'dovich (SZ) flux, the X-ray analogue of the SZ flux ($Y_X$) and the hydrostatic mass. For the most realistic models, which include AGN feedback, the slopes of the various mass-observable relations deviate substantially from the self-similar ones, particularly at late times and for low-mass clusters. The amplitude of the mass-temperature relation shows negative evolution with respect to the self-similar prediction (i.e. slower than the prediction) for all models, driven by an increase in non-thermal pressure support at higher redshifts. The AGN models predict strong positive evolution of the gas mass fractions at low halo masses. The SZ flux and $Y_X$ show positive evolution with respect to self-similarity at low mass but negative evolution at high mass. The scatter about the relations is well approximated by log-normal distributions, with widths that depend mildly on halo mass. The scatter decreases significantly with increasing redshift. The exception is the hydrostatic mass-halo mass relation, for which the scatter increases with redshift. Finally, we discuss the relative merits of various hot gas-based mass proxies.

The redshift evolution of massive galaxy clusters in the MACSIS simulations

We present the MAssive ClusterS and Intercluster Structures (MACSIS) project, a suite of 390 clusters simulated with baryonic physics that yields realistic massive galaxy clusters capable of matching a wide range of observed properties. MACSIS extends the recent BAHAMAS simulation to higher masses, enabling robust predictions for the redshift evolution of cluster properties and an assessment of the effect of selecting only the hottest systems. We study the observable-mass scaling relations and the X-ray luminosity-temperature relation over the complete observed cluster mass range. As expected, we find the slope of these scaling relations and the evolution of their normalization with redshift departs significantly from the self-similar predictions. However, for a sample of hot clusters with core-excised temperatures $k_{\rm{B}}T\geq5\,\rm{keV}$ the normalization and slope of the observable-mass relations and their evolution are significantly closer to self-similar. The exception is the temperature-mass relation, for which the increased importance of non-thermal pressure support and biased X-ray temperatures leads to a greater departure from self-similarity in the hottest systems. As a consequence, these also affect the slope and evolution of the normalization in the luminosity-temperature relation. The median hot gas profiles show good agreement with observational data at $z=0$ and $z=1$, with their evolution again departing significantly from the self-similar prediction. However, selecting a hot sample of clusters yields profiles that evolve significantly closer to the self-similar prediction. In conclusion, our results show that understanding the selection function is vital for robust calibration of cluster properties with mass and redshift.