Revisiting the missing mass problem in MOND for nearby galaxy clusters

TL;DR

The paper tackles the MOND missing mass problem in galaxy clusters by recalculating cluster baryons with the IGIMF, which links the galaxy-wide IMF to star-formation rate and metallicity and yields a large population of stellar remnants in massive ellipticals. By combining IGIMF-based stellar masses with ICL and ICM data from 46 nearby clusters (plus NGC 5044), the authors show that total baryonic mass can reach about $88^{+5+2}_{-4-1}\%$ of the MOND dynamical mass, substantially alleviating the missing mass issue. The analysis uses X-ray gas masses, hydrostatic-equilibrium–based dynamical masses, and a robust handling of observational ICL fractions, while discussing potential tensions with independent lensing and RAR constraints and proposing remnant kick-velocity–driven spatial distributions as a plausible reconciliation. The work highlights IGIMF as a route to reconciling MOND with cluster dynamics, while noting remaining uncertainties in ICL estimates and remnant demographics that warrant future spatially resolved modeling and cross-method validation.

Abstract

In the framework of Milgromian dynamics (MOND), galaxy clusters are known to exhibit a residual missing mass problem, with the baryonic mass falling short of the dynamical mass by about a factor of two. The baryon content of clusters is dominated by the intracluster medium (ICM), while the stellar contribution depends sensitively on the assumed stellar initial mass function (IMF). We re-evaluate the stellar and remnant masses in galaxy clusters by adopting the integrated galaxy-wide initial mass function (IGIMF) theory, which accounts for the dependence of the IMF on galaxy properties and star formation histories. Massive elliptical galaxies, characterized by high metallicities and short formation timescales, are inferred to form with top-heavy IMFs, leading to a substantial population of stellar remnants. Using observational data from WINGS and 2MASS for 46 nearby (z < 0.1) galaxy clusters, we compute stellar, remnant, and intracluster light masses and combine them with previously derived ICM masses. The resulting total baryonic masses are compared to MOND dynamical masses inferred from hydrostatic equilibrium. We find that the baryonic mass in stars, remnants and the ICM accounts for at least $88^{+5+2}_{-4-1}\%$ of the MOND dynamical mass. This constrains the kick velocities of the remnants and substantially alleviates the missing mass problem for galaxy clusters in MOND.

Figures (26)

• Figure 1: The relation between $M/L$ ratios and luminosities in the B-band at redshift $z = 0$. Upper plot: The relation for elliptical galaxies. The blue dots are the $M/L$ values in the IGIMF theory, the blue line is the result of cubic spline interpolation to the blue dots. The red dots are the $M/L$ values in the canonical IMF Theory, the red line is the result of cubic spline interpolation to the red dots. Lower plot: the relation for spiral galaxies, otherwise as above.
• Figure 2: The B-band luminosity distribution of member galaxies in the galaxy cluster Abell 85. The orange histogram represents the number distribution of elliptical (E+dE) and S0 (S0+dS0) galaxies, while the blue histogram shows the number distribution of all other types of galaxies. Apparent magnitudes are from d2014surface, while the morphologies are from fasano2012morphology.
• Figure 3: The B-band luminosity distribution of member galaxies in the galaxy group NGC 5044. The orange histogram shows the number distribution of elliptical and S0 galaxies, the blue histogram shows the number distribution of all other galaxy types. Data are from mendel2008anatomy.
• Figure 4: Total galaxy masses, $M_{\rm gal}$, of 19 common clusters vs their MOND dynamical masses, $M_{\rm dyn}$, in the canonical IMF (upper panel) and IGIMF (lower panel) framework. Blue dots are in the WINGS B-band, black dots are WINGS V-band d2014surfacefasano2012morphology, red dots are 2MASS K-band lin2004klin2004kk. The auxiliary horizontal and vertical lines serve to emphasise the scale relationship relative to $10^{14}M_{\odot}$. Note that all MOND dynamical masses are from brownstein2006galaxy.
• Figure 5: Mass relation of WINGS clusters in the canonical IMF case. The x-axis represents the MOND dynamical masses of the individual galaxy clusters brownstein2006galaxy. The y-axis represents the individual mass components in units of the MOND dynamical mass. The black dots are the MOND dynamical masses, $M_{\rm dyn}$; the blue dots are the gas masses, $M_{\rm gas}$; the green dots are the gas + galaxy masses, $M_{\rm gas+gal}$; and the red dots are the gas + galaxy + ICL (total baryonic) mass, $M_{\rm bar}$ (error bars do not account for the ICL mass uncertainty). The auxiliary horizontal and vertical lines serve to emphasise the scale relationship relative to $M/M_{\rm dyn}$ and $10^{14}M_{\odot}$, respectively. The red shaded region represents the error range of total baryonic mass after including the systematic uncertainty from the ICL. All error bars are derived from the error propagation of $M/M_{\rm dyn}$.