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Register a new userThe Redshift Evolution of the Tully-Fisher Relation as a Test of Modified Gravity
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The redshift evolution of the Tully-Fisher Relation probes gravitational dynamics that must be consistent with any modified gravity theory seeking to explain the galactic rotation curves without the need for dark matter. Within the context of non-relativistic Modified Newtonian Dynamics (MOND), the characteristic acceleration scale of the theory appears to be related to the current value of either the Hubble constant, i.e., alpha ~ cH_0, or the dark energy density, i.e., alpha (8 pi G rho_lambda/3)^{1/2}. If these relations are the manifestation of a fundamental coupling of a_0 to either of the two cosmological parameters, the cosmological evolution would then dictate a particular dependence of the MOND acceleration scale with redshift that can be tested with Tully-Fisher relations of high-redshift galaxies. We compare this prediction to two sets of Tully-Fisher data with redshifts up to z=1.2. We find that both couplings are excluded within the formal uncertainties. However, when we take into account the potential systematic uncertainties in the data, we find that they marginally favor the coupling of the MOND acceleration scale to the density of dark energy.
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We test the Grumillers quantum motivated modified gravity model, which at large distances modifies the Newtonian potential and describes the galactic rotation curves of disk galaxies in terms of a Rindler acceleration term without the need of any dark matter, against the baryonic Tully-Fisher feature that relates the total baryonic mass of a galaxy with flat rotation velocity of the galaxy. We estimate the Rindler acceleration parameter from observed baryonic mass versus rotation velocity data of a sample of sixty galaxies. Grumillers model is found to describe the observed data reasonably well.
The Tully-Fisher Relation (TFR) links two fundamental properties of disk galaxies: their luminosity and their rotation velocity (mass). The pioneering work of Vogt et al. in the 1990s showed that it is possible to study the TFR for spiral galaxies at considerable look-back-times, and use it as a powerful probe of their evolution. In recent years, several groups have studied the TFR for galaxies in different environments reaching redshifts beyond one. In this brief review I summarise the main results of some of these studies and their consequences for our understanding of the formation and evolution of disk galaxies. Particular emphasis is placed on the possible environment-driven differences in the behaviour of the TFR for field and cluster galaxies.
We present the B-band Tully-Fisher relation (TFR) of 60 late-type galaxies with redshifts 0.1-1. The galaxies were selected from the FORS Deep Field with a limiting magnitude of R=23. Spatially resolved rotation curves were derived from spectra obtained with FORS2 at the VLT. High-mass galaxies with v_max>=150 km/s show little evolution, whereas the least massive systems in our sample are brighter by about 1-2 mag compared to their local counterparts. For the entire distant sample, the TFR slope is flatter than for local field galaxies (-5.77+-0.45 versus -7.92+-0.18). Thus, we find evidence for evolution of the slope of the TFR with redshift on the 3-sigma level. This is still true when we subdivide the sample into three redshift bins. We speculate that the flatter tilt of our sample is caused by the evolution of luminosities and an additional population of blue galaxies at z>=0.2. The mass dependence of the TFR evolution also leads to variations for different galaxy types in magnitude-limited samples, suggesting that selection effects can account for the discrepant results of previous TFR studies on the luminosity evolution of late-type galaxies.
We analyse the Tully-Fisher relation at moderate redshift from the point of view of the underlying stellar populations, by comparing optical and NIR photometry with a phenomenological model that combines population synthesis with a simple prescription for chemical enrichment. The sample comprises 108 late-type galaxies extracted from the FORS Deep Field (FDF) and William Herschel Deep Field (WHDF) surveys at z<1 (median redshift z=0.45). A correlation is found between stellar mass and the parameters that describe the star formation history, with massive galaxies forming their populations early (zFOR~3), with star formation timescales, tau1~4Gyr; although with very efficient chemical enrichment timescales (tau2~1Gyr). In contrast, the stellar-to-dynamical mass ratio - which, in principle, would track the efficiency of feedback in the baryonic processes driving galaxy formation - does not appear to correlate with the model parameters. On the Tully-Fisher plane, no significant age segregation is found at fixed circular speed, whereas at fixed stellar-to-dynamical mass fraction, age splits the sample, with older galaxies having faster circular speeds at fixed Ms/Mdyn. Although our model does not introduce any prior constraint on dust reddening, we obtain a strong correlation between colour excess and stellar mass.
We investigate the stellar-mass Tully-Fisher relation (TFR) between the stellar mass and the integrated gas velocity dispersion, quantified by the kinematic estimator S_0.5 measured from strong emission lines in spectra of galaxies at 0<z<5. We combine luminosity-selected galaxies (`high-luminosity sample) with galaxies selected in other ways (`low-luminosity sample) to cover a range in stellar mass that spans almost five orders of magnitude: 7.0 < log M* < 11.5. We find that the logarithmic power-law slope and normalisation of the TFR are independent of redshift out to z~3. The scatter in the TFR is <0.5 dex such that the gas velocity dispersion can be used as a proxy for the stellar mass of a galaxy independently of its redshift. At z>3 the scatter increases and the existence of a correlation is not obvious. The high-luminosity sample exhibits a flatter slope of 1.5$pm$0.2 at z<3 compared to the low-luminosity sample slope of 2.9$pm$0.3, suggesting a turnover in the TFR. The combined sample is well fit with a break in the TFR at a characteristic stellar mass scale of M*~10$^{10}$ M$_{odot}$, with no significant evolution out to z~3. We demonstrate that a break in the TFR with a steeper slope at the low-mass end is a natural consequence of galaxy models with a mass-dependent stellar to halo-mass ratio.
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