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Register a new userCalibrated Tully-Fisher relations for improved estimates of disk rotation velocities
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R. Reyes
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In this paper, we derive scaling relations between photometric observable quantities and disk galaxy rotation velocity V_rot, or Tully-Fisher relations (TFRs). Our methodology is dictated by our purpose of obtaining purely photometric, minimal-scatter estimators of V_rot applicable to large galaxy samples from imaging surveys. To achieve this goal, we have constructed a sample of 189 disk galaxies at redshifts z<0.1 with long-slit H-alpha spectroscopy from Pizagno et al. (2007) and new observations. By construction, this sample is a fair subsample of a large, well-defined parent disk sample of ~170 000 galaxies selected from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). The optimal photometric estimator of V_rot we find is stellar mass M_* from Bell et al. (2003), based on the linear combination of a luminosity and a colour. Assuming a Kroupa IMF, we find: log [V_{80}/(km s^-1)] = (2.142 +/- 0.004)+(0.278 +/- 0.010)[log (M_*/M_sun)-10.10], where V_{80} is the rotation velocity measured at the radius R_{80} containing 80 per cent of the i-band galaxy light. This relation has an intrinsic Gaussian scatter of 0.036 +/- 0.005 dex and a measured scatter of 0.056 dex in log V_{80}. For a fixed IMF, we find that the dynamical-to-stellar mass ratios within R_{80}, (M_dyn/M_*)(R_{80}), decrease from approximately 10 to 3, as stellar mass increases from M_* ~ 10^9 to 10^{11} M_sun. At a fixed stellar mass, (M_dyn/M_*)(R_{80}) increases with disk size, so that it correlates more tightly with stellar surface density than with stellar mass or disk size alone. In future work, we will use these results to study disk galaxy formation and evolution, and perform a fair, statistical analysis of the dynamics and masses of a photometrically-selected sample of disk galaxies. [Abridged]
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Power-law relations between tracers of baryonic mass and rotational velocities of disk galaxies, so-called Tully-Fisher relations (TFRs), offer a wealth of applications in galaxy evolution and cosmology. However, measurements of rotational velocities require galaxy inclinations, which are difficult to measure, thus limiting the range of TFR studies. This work introduces a maximum likelihood estimation (MLE) method for recovering the TFR in galaxy samples with limited or no information on inclinations. The robustness and accuracy of this method is demonstrated using virtual and real galaxy samples. Intriguingly, the MLE reliably recovers the TFR of all test samples, even without using any inclination measurements - that is, assuming a sin(i)-distribution for galaxy inclinations. Explicitly, this inclination-free MLE recovers the three TFR parameters (zero-point, slope, scatter) with statistical errors only about 1.5-times larger than the best estimates based on perfectly known galaxy inclinations with zero uncertainty. Thus, given realistic uncertainties, the inclination-free MLE is highly competitive. If inclination measurements have mean errors larger than 10 degrees, it is better not to use any inclinations, than to consider the inclination measurements to be exact. The inclination-free MLE opens interesting perspectives for future HI surveys by the SKA and its pathfinders.
We present a new technique for the statistical evaluation of the Tully-Fisher relation (TFR) using spectral line stacking. This technique has the potential to extend TFR observations to lower masses and higher redshifts than possible through a galaxy-by-galaxy analysis. It further avoids the need for individual galaxy inclination measurements. To quantify the properties of stacked HI emission lines, we consider a simplistic model of galactic disks with analytically expressible line profiles. Using this model, we compare the widths of stacked profiles with those of individual galaxies. We then follow the same procedure using more realistic mock galaxies drawn from the S3-SAX model (a derivative of the Millennium simulation). Remarkably, when stacking the apparent HI lines of galaxies with similar absolute magnitude and random inclinations, the width of the stack is very similar to the width of the deprojected (= corrected for inclination) and dedispersed (= after removal of velocity dispersion) input lines. Therefore, the ratio between the widths of the stack and the deprojected/dedispersed input lines is approximately constant - about 0.93 - with very little dependence on the gas dispersion, galaxy mass, galaxy morphology, and shape of the rotation curve. Finally, we apply our technique to construct a stacked TFR using HIPASS data which already has a well defined TFR based on individual detections. We obtain a B-band TFR with a slope of $-8.5pm0.4$ and a K-band relation with a slope of $-11.7pm0.6$ for the HIPASS data set which is consistent with the existing results.
We compare the Baryonic Tully-Fisher relation (BTFR) of simulations and observations of galaxies ranging from dwarfs to spirals, using various measures of rotational velocity Vrot. We explore the BTFR when measuring Vrot at the flat part of the rotation curve, Vflat, at the extent of HI gas, Vlast, and using 20% (W20) and 50% (W50) of the width of HI line profiles. We also compare with the maximum circular velocity of the parent halo, Vmax, within dark matter only simulations. The different BTFRs increasingly diverge as galaxy mass decreases. Using Vlast one obtains a power law over four orders of magnitude in baryonic mass, with slope similar to the observed BTFR. Measuring Vflat gives similar results as Vlast when galaxies with rising rotation curves are excluded. However, higher rotation velocities would be found for low mass galaxies if the cold gas extended far enough for Vrot to reach a maximum. W20 gives a similar slope as Vlast but with slightly lower values of Vrot for low mass galaxies, although this may depend on the extent of the gas in your galaxy sample. W50 bends away from these other relations toward low velocities at low masses. By contrast, Vmax bends toward high velocities for low mass galaxies, as cold gas does not extend out to the radius at which halos reach Vmax. Our study highlights the need for careful comparisons between observations and models: one needs to be consistent about the particular method of measuring Vrot, and precise about the radius at which velocities are measured.
We demonstrate that the comparison of Tully-Fisher relations (TFRs) derived from global HI line widths to TFRs derived from the circular velocity profiles of dynamical models (or stellar kinematic observations corrected for asymmetric drift) is vulnerable to systematic and uncertain biases introduced by the different measures of rotation used. We therefore argue that to constrain the relative locations of the TFRs of spiral and S0 galaxies, the same tracer and measure must be used for both samples. Using detailed near-infrared imaging and the circular velocities of axisymmetric Jeans models of 14 nearby edge-on Sa-Sb spirals and 14 nearby edge-on S0s drawn from a range of environments, we find that S0s lie on a TFR with the same slope as the spirals, but are on average 0.53+/-0.15 mag fainter at Ks-band at a given rotational velocity. This is a significantly smaller offset than that measured in earlier studies of the S0 TFR, which we attribute to our elimination of the bias associated with using different rotation measures and our use of earlier type spirals as a reference. Since our measurement of the offset avoids systematic biases, it should be preferred to previous estimates. A spiral stellar population in which star formation is truncated would take ~1 Gyr to fade by 0.53 mag at Ks-band. If S0s are the products of a simple truncation of star formation in spirals, then this finding is difficult to reconcile with the observed evolution of the spiral/S0 fraction with redshift. Recent star formation could explain the observed lack of fading in S0s, but the offset of the S0 TFR persists as a function of both stellar and dynamical mass. We show that the offset of the S0 TFR could therefore be explained by a systematic difference between the total mass distributions of S0s and spirals, in the sense that S0s need to be smaller or more concentrated than spirals.
The Tully-Fisher (TF) or the luminosity line-width relations of the galaxies in the Eridanus group are constructed using the HI rotation curves and the luminosities in the optical and in the near-infrared bands. The slopes of the TF relations (absolute magnitude vs log2V_{flat}) are -8.6pm1.1, -10.0pm1.5, -10.7pm2.1, and -9.7pm1.3 in the R, J, H, and K bands respectively for galaxies having flat HI rotation curves. These values of the slopes are consistent with those obtained from studies of other groups and clusters. The scatter in the TF relations is in the range 0.5 - 1.1 mag in different bands. This scatter is considerably larger compared to those observed in other groups and clusters. It is suggested that the larger scatter in the TF relations for the Eridanus group is related to the loose structure of the group. If the TF relations are constructed using the baryonic mass (stellar + HI + Helium mass) instead of the stellar luminosity, nearly identical slopes are obtained in the R and in the near-infrared bands. The baryonic TF (baryonic mass vs log2V_{flat}) slope is in the range 3.5 - 4.1.
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