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Register a new userA new formulation of the external field effect in MOND and numerical simulations of ultra-diffuse dwarf galaxies $-$ application to NGC 1052-DF2 and NGC 1052-DF4
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The ultra-diffuse dwarf galaxy NGC 1052-DF2 (DF2) has ten (eleven) measured globular clusters (GCs) with a line-of-sight velocity dispersion of $sigma=7.8^{+5.2}_{-2.2},$km/s ($sigma=10.6^{+3.9}_{-2.3},$km/s). Our conventional statistical analysis of the original ten GCs gives $sigma=8.0^{+4.3}_{-3.0},$km/s. The overall distribution of velocities agrees well with a Gaussian of this width. Due to the non-linear Poisson equation in MOND, a dwarf galaxy has weaker self-gravity when in close proximity to a massive host. This external field effect is investigated using a new analytic formulation and fully self-consistent live $N$-body models in MOND. Our formulation agrees well with that of Famaey and McGaugh (2012). These new simulations confirm our analytic results and suggest that DF2 may be in a deep-freeze state unique to MOND. The correctly calculated MOND velocity dispersion agrees with our inferred dispersion and that of van Dokkum et al. (2018b) if DF2 is within 150 kpc of NGC 1052 and both are 20 Mpc away. The GCs of DF2 are however significantly brighter and larger than normal GCs, a problem which disappears if DF2 is significantly closer to us. A distance of 10-13 Mpc makes DF2 a normal dwarf galaxy even more consistent with MOND and the 13 Mpc distance reported by Trujillo et. al. (2019). We discuss the similar dwarf DF4, finding good agreement with MOND. We also discuss possible massive galaxies near DF2 and DF4 along with their distances and peculiar velocities, noting that NGC 1052 may lie at a distance near 10 Mpc.
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Recently van Dokkum et al. (2018b) reported that the galaxy NGC 1052-DF2 (DF2) lacks dark matter if located at $20$ Mpc from Earth. In contrast, DF2 is a dark-matter-dominated dwarf galaxy with a normal globular cluster population if it has a much shorter distance near $10$ Mpc. However, DF2 then has a high peculiar velocity wrt. the cosmic microwave background of $886$ $rm{km,s^{-1}}$, which differs from that of the Local Group (LG) velocity vector by $1298$ $rm{km,s^{-1}}$ with an angle of $117 , ^{circ}$. Taking into account the dynamical $M/L$ ratio, the stellar mass, half-light radius, peculiar velocity, motion relative to the LG, and the luminosities of the globular clusters, we show that the probability of finding DF2-like galaxies in the lambda cold dark matter ($Lambda$CDM) TNG100-1 simulation is at most $1.0times10^{-4}$ at $11.5$ Mpc and is $4.8times10^{-7}$ at $20.0$ Mpc. At $11.5$ Mpc, the peculiar velocity is in significant tension with the TNG100-1, TNG300-1, and Millennium simulations, but occurs naturally in a Milgromian cosmology. At $20.0$ Mpc, the unusual globular cluster population would challenge any cosmological model. Estimating that precise measurements of the internal velocity dispersion, stellar mass, and distance exist for $100$ galaxies, DF2 is in $2.6sigma$ ($11.5$ Mpc) and $4.1sigma$ ($20.0$ Mpc) tension with standard cosmology. Adopting the former distance for DF2 and assuming that NGC 1052-DF4 is at $20.0$ Mpc, the existence of both is in tension at $geq4.8sigma$ with the $Lambda$CDM model. If both galaxies are at $20.0$ Mpc the $Lambda$CDM cosmology has to be rejected by $geq5.8sigma$.
NGC 1052-DF2, an ultra diffuse galaxy (UDG), has been the subject of intense debate. Its alleged absence of dark matter, and the brightness and number excess of its globular clusters (GCs) at an initially assumed distance of 20Mpc, suggested a new formation channel for UDGs. We present the first systematic spectroscopic analysis of both the stellar body and the GCs (six of which were previously known, and one newly confirmed member) of this galaxy using MUSE@VLT. Even though NGC 1052-DF2 does not show any spatially extended emission lines we report the discovery of three planetary nebulae (PNe). We conduct full spectral fitting on the UDG and the stacked spectra of all GCs. The UDGs stellar population is old, 8.9$pm$1.5 Gyr, metal-poor, with [M/H] = $-$1.07$pm$0.12 with little or no $alpha$-enrichment. The stacked spectrum of all GCs indicates a similar age of 8.9$pm$1.8 Gyr, but lower metallicity, with [M/H] = $-$1.63$pm$0.09, and similarly low $alpha$-enrichment. There is no evidence for a variation of age and metallicity in the GC population with the available spectra. The significantly more metal-rich stellar body with respect to its associated GCs, the age of the population, its metallicity and alpha enrichment, are all in line with other dwarf galaxies. NGC 1052-DF2 thus falls on the same empirical mass-metallicity relation as other dwarfs, for the full distance range assumed in the literature. We find that both debated distance estimates (13 and 20 Mpc) are similarly likely, given the three discovered PNe.
The so-called ultra-diffuse galaxy NGC~1052-DF2 was announced to be a galaxy lacking dark matter based on a spectroscopic study of its constituent globular clusters. Here we present the first spectroscopic analysis of the stellar body of this galaxy using the MUSE integral-field spectrograph at the (ESO) Very Large Telescope. The MUSE datacube simultaneously provides DF2s stellar velocity field and systemic velocities for seven globular clusters (GCs). We further discovered three planetary nebulae (PNe) that are likely part of this galaxy. While five of the clusters had velocities measured in the literature, we were able to confirm the membership of two more candidates through precise radial velocity measurements, which increases the measured specific frequency of GCs in DF2. The mean velocity of the diffuse stellar body, 1792.9$^{-1.8}_{+1.4}$~kms, is consistent with the mean globular cluster velocity. We detect a weak but significant velocity gradient within the stellar body, with a kinematic axis close to the photometric major-axis, making it a prolate-like rotator. We estimate a velocity dispersion from the clusters and PNe of $sigma_{mathrm{int}}=10.6^{+3.9}_{-2.3}$~kms. The velocity dispersion $sigma_{rm{DF2}star}$(re) for the stellar body within one effective radius is $10.8^{-4.0}_{+3.2}$~kms. Considering various sources of systemic uncertainties this central value varies between 5 and 13~kms, and we conservatively report a 95% confidence upper limit to the dispersion within one re of 21~kms. We provide updated mass estimates based on these dispersions corresponding to the different distances to NGC~1052-DF2 that have been reported in the recent literature.
Based upon the kinematics of ten globular clusters, it has recently been claimed that the ultra-diffuse galaxy, NCD 1052-DF2, lacks a significant quantity of dark matter. Dynamical analyses have generally assumed that this galaxy is pressure supported, with the relatively small velocity dispersion of the globular cluster population indicating the deficit of dark matter. However, the presence of a significant rotation of the globular cluster population could substantially modify this conclusion. Here we present the discovery of such a signature of rotation in the kinematics of NGC 1052-DF2s globular clusters, with a velocity amplitude of $sim12.44^{+4.40}_{-5.16}$ km/s, which, through Bayesian model comparison, represents a marginally better fit to the available kinematic data; note that this rotation is distinct from, and approximately perpendicular to, the recently identified rotation of the stellar component of NGC 1052-DF2. Assuming this truly represents an underlying rotation, it is shown that the determined mass depends upon the inclination of the rotational component and, with a moderate inclination, the resultant mass to light ratio can exceed $M/Lsim10$.
Using ultra-deep imaging ($mu_g = 30.4$ mag/arcsec$^2$; 3$sigma$, 10x10), we probed the surroundings of the first galaxy lacking dark matter KKS2000[04] (NGC 1052-DF2). Signs of tidal stripping in this galaxy would explain its claimed low content of dark matter. However, we find no evidence of tidal tails. In fact, the galaxy remains undisturbed down to a radial distance of 80 arcsec. This radial distance triples previous spatial explorations of the stellar distribution of this galaxy. In addition, the distribution of its globular clusters (GCs) is not extended in relation to the bulk of the galaxy (the radius containing half of the GCs is 21 arcsec). We also found that the surface brightness radial profiles of this galaxy in the g and r bands decline exponentially from 35 to 80 arcsec. That, together with a constant ellipticity and position angle in the outer parts of the galaxy strongly suggests the presence of a low-inclination disk. This is consistent with the evidence of rotation found for this object. This finding implies that the dynamical mass of this galaxy is a factor of 2 higher than previously reported, bringing the dark matter content of this galaxy in line with galaxies of similar stellar mass.
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