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Register a new userResponse of the integrals in the Tremaine-Weinberg method to multiple pattern speeds: a counter-rotating inner bar in NGC 2950?
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Authors
Witold Maciejewski
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When integrals in the standard Tremaine-Weinberg method are evaluated for the case of a realistic model of a doubly barred galaxy, their modifications introduced by the second rotating pattern are in accord with what can be derived from a simple extension of that method, based on separation of tracers density. This extension yields a qualitative argument that discriminates between prograde and retrograde inner bars. However, the estimate of the value of inner bars pattern speed requires further assumptions. When this extension of the Tremaine-Weinberg method is applied to the recent observation of the doubly barred galaxy NGC 2950, it indicates that the inner bar there is counter-rotating, possibly with the pattern speed of -140 +/- 50 km/s/arcsec. The occurrence of counter-rotating inner bars can constrain theories of galaxy formation.
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We apply the Tremaine-Weinberg method to 19 nearby galaxies using stellar mass surface densities and velocities derived from the PHANGS-MUSE survey, to calculate (primarily bar) pattern speeds ($Omega_{rm P}$). After quality checks, we find that around half (10) of these stellar mass-based measurements are reliable. For those galaxies, we find good agreement between our results and previously published pattern speeds, and use rotation curves to calculate major resonance locations (co-rotation radii and Lindblad resonances). We also compare these stellar-mass derived pattern speeds with H$alpha$ (from MUSE) and CO($J=2{-}1$) emission from the PHANGS-ALMA survey. We find that in the case of these clumpy ISM tracers, this method erroneously gives a signal that is simply the angular frequency at a representative radius set by the distribution of these clumps ($Omega_{rm clump}$), and that this $Omega_{rm clump}$ is significantly different to $Omega_{rm P}$ ($sim$20% in the case of H$alpha$, and $sim$50% in the case of CO). Thus, we conclude that it is inadvisable to use pattern speeds derived from ISM kinematics. Finally, we compare our derived pattern speeds and co-rotation radii, along with bar properties, to the global parameters of these galaxies. Consistent with previous studies, we find that galaxies with a later Hubble type have a larger ratio of co-rotation radius to bar length, more molecular-gas rich galaxies have higher $Omega_{rm P}$, and more bulge-dominated galaxies have lower $Omega_{rm P}$. Unlike earlier works, however, there are no clear trends between the bar strength and $Omega_{rm P}$, nor between the total stellar mass surface density and the pattern speed.
We present surface photometry and stellar kinematics of NGC 2950, which is a nearby and undisturbed SB0 galaxy hosting two nested stellar bars. We use the Tremaine-Weinberg method to measure the pattern speed of the primary bar. This also permits us to establish directly and for the first time that the two nested bars are rotating with different pattern speeds, and in particular that the rotation frequency of the secondary bar is higher than that of the primary one.
Estimating the bar pattern speed (Om{}) is one of the main challenges faced in understanding the role of stellar bars in galaxy dynamical evolution. This work aims to characterise different uncertainty sources affecting the Tremaine Weinberg (TW)-method to study the correlation between bar and galaxies physical parameters. We use a sample of 15 MaNGA SDSS-IV galaxies and 3 CALIFA galaxies from cite{Aguerri2015}. We studied the errors related with (i) galaxy centre determination, (ii) disc position angle (PA) emphasising the difficulties triggered by outer non-axisymmetric structures besides the bar, (iii) the slits length and (iv) the spatial resolution. In average, the PA uncertainties range $sim 15 %$, the slit length $sim 9 %$ and the centring error $sim 5 %$. Reducing the spatial resolution increases the sensitivity to the PA error. Through Monte Carlo simulations, we estimate the probability distribution of the R{} bar speed parameter. The present sample is composed of 7 slow, 4 fast and 7 ultrafast bars, with no trend with morphological types. Although uncertainties and low sample numbers may mask potential correlations between physical properties, we present a discussion of them: We observe an anti-correlation of Om{} with the bar length and the stellar mass, suggesting that massive galaxies tend to host longer and slower bars. We also observe a correlation of the molecular gas fraction with R{}, and a weak anti-correlation with Om{}, suggesting that bars rotate slower in gaseous discs. Confirmation of such trends awaits future studies.
At the intersection of galactic dynamics, evolution and global structure, issues such as the relation between bars and spirals and the persistence of spiral patterns can be addressed through the characterization of the angular speeds of the patterns and their possible radial variation. The Radial Tremaine-Weinberg (TWR) Method, a generalized version of the Tremaine-Weinberg method for observationally determining a single, constant pattern speed, allows the pattern speed to vary arbitrarily with radius. Here, we perform tests of the TWR method with regularization on several simulated galaxy data sets. The regularization is employed as a means of smoothing intrinsically noisy solutions, as well as for testing model solutions of different radial dependence (e.g. constant, linear or quadratic). We test these facilities in studies of individual simulations, and demonstrate successful measurement of both bar and spiral pattern speeds in a single disk, secondary bar pattern speeds, and spiral winding (in the first application of a TW calculation to a spiral simulation). We also explore the major sources of error in the calculation and find uncertainty in the major axis position angle most dominant. In all cases, the method is able to extract pattern speed solutions where discernible patterns exist to within 20% of the known values, suggesting that the TWR method should be a valuable tool in the area of galactic dynamics. For utility, we also discuss the caveats in, and compile a prescription for, applications to real galaxies.
We report on our attempts to achieve a nearly steady-state gas flow in hydrodynamical simulations of doubly barred galaxies. After exploring the parameter space, we construct two models, for which we evaluate the photometric and the kinematic integrals, present in the Tremaine-Weinberg method, in search of observational signatures of two rotating patterns. We show that such signatures are often present, but a direct fit to data points is likely to return incorrect pattern speeds. However, for a particular distribution of the tracer, presented here, the values of the pattern speeds can be retrieved reliably even with the direct fit.
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