We measured the galactic hydrogen column densities to the neutron-star binaries GX 17+2, 4U 1705-44, and 4U 1728-34 by modeling the Mg and Si absorption edges found in high-resolution X-ray spectra obtained by the Chandra X-ray Observatory. We found
for GX 17+2, N_H = (2.38 +/- 0.12) x 10^22 cm^-2, for 4U 1705-44, N_H = (2.44 +/- 0.09) x 10^22 cm^-2, and for 4U 1728-34, N_H = (2.49 +/- 0.14) x 10^22 cm^-2. These values are in reasonable agreement with the hydrogen column densities inferred earlier from modeling of the continuum spectra of the sources. Our results can be used to constrain the uncertainties of model parameters of the X-ray spectra of these sources that are correlated to the uncertainties of the hydrogen column density. In the case of continuum spectra obtained during thermonuclear X-ray bursts, they will significantly reduce the uncertainties in the spectroscopically measured masses and radii of the neutron stars.
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-rel
ativistic 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.
