The SAMI Galaxy Survey:
Towards a unified dynamical scaling relation for galaxies of all types

We focus on the first 304 galaxies observed by SAMI in the footprint of the Galaxy And Mass Assembly Survey (GAMA, Driver et al. 2011) for the wealth of multiwavelength data available (see § 2.3).

Observations were carried out on March 5-17 and April 12-16, 2013. The typical observing strategy consists of seven dithered observations totalling 3.5 hours to achieve near-uniform spatial coverage across each hexabundle. The AAOmega data reduction pipeline 2dfdr was used to perform all the standard data reduction steps. Flux calibration was done taking advantage of a spectro-photometric standard star observed during the same night, while correction for telluric absorption was made using simultaneous observations of a secondary standard star (included in the same SAMI plate of the target). The row-stacked spectra of each exposure generated by 2dfdr were then combined, reconstructed into an image and resampled on a Cartesian grid of 0.5″$\times$0.5″spaxel size (see Sharp et al. 2014 and Allen et al. 2014 for more details).

To obtain homogenous global rotation and dispersion velocities for both gas and stars within one effective radius ($r_{e}$), we select the 250 galaxies in our sample with an $r$-band effective diameter (see § 2.3) smaller than the size of a SAMI hexabundle (14.7″), and greater than the typical spatial resolution of our observations (2.5″, i.e., $\sim$2.1 kpc at the average redshift of our sample, see also Allen et al. 2014). The average diameter of our sample is $\sim$8″.

Stellar line-of-sight velocity and intrinsic dispersion maps were then obtained using the penalised pixel-fitting routine ppxf, developed by Cappellari & Emsellem (2004), following the same pixel-by-pixel technique described in Fogarty et al. (2014).

Gas velocity maps were created from the reduced data cubes using the new lzifu IDL fitting routine (Ho et al. in prep.; see also Ho et al. 2014). After subtracting the stellar continuum with ppxf, lzifu models the emission lines in each spaxel as Gaussians and performs a non-linear least-square fit using the Levenberg-Marquardt method. We fit up to 11 strong optical emission lines ([Oii]$\lambda\lambda$3726,29, H$\beta$, [Oiii]$\lambda\lambda$4959,5007, [Oi]$\lambda$6300, [Nii]$\lambda\lambda$6548,83, H$\alpha$, and [Sii]$\lambda\lambda$6716,31) simultaneously, constraining all the lines to share the same rotation velocity and dispersion. Each line is modelled as a single-component Gaussian (including the effect of instrumental resolution; e.g., Weiner et al. 2006), and we use the reconstructed kinematic maps to measure gas rotation and intrinsic velocity dispersion.

We then select our final sample as follows. First, spaxels are discarded if the fit failed or if the error on the velocities is greater than 20 km s^-1 and 50 km s^-1 for gas and stars, respectively. This conservative cut roughly corresponds to one third of spectral FWHM in SAMI cubes. Second, we estimate the fraction of ‘good’ spaxels ($f$) left within an ellipse of semi-major axis $r_{e}$ and ellipticity and position angle determined from optical $r$-band Sloan Digital Sky Survey (SDSS, York et al. 2000) images (see § 2.3), and reject those galaxies with $f<$80%. This selection guarantees that we are properly tracing the galaxy kinematics up to $r_{e}$, and it leaves us with 235 individual galaxies: 193 with gas kinematics, 105 with stellar kinematics and 62 with both (see Fig. 1). Although our analysis takes advantage of less than 10% of the final SAMI Galaxy Survey, the sample size is already comparable to the largest IFU surveys of nearby galaxies to date (Cappellari et al. 2011; Sánchez et al. 2012). The properties of our final sample are summarised in Fig. 1.

Stellar and gas velocity widths ($W$) are obtained from the velocity histogram created by combining all the ‘good’ spaxels within $r_{e}$. Following the standard technique used for H$\alpha$ rotation curves, we define $W$ as the difference between the 90th and 10th percentile points of the velocity histogram ($W=V_{90}-V_{10}$, Catinella et al. 2005). We adopt the velocity histogram technique because this is the simplest method to determine velocity widths, making our results easily comparable to other studies, including long-slit spectroscopy. Rotational velocities are then computed as

where $i$ is the galaxy inclination and $z$ is the redshift. Inclinations are determined from the $r$-band minor-to-major axis ratio ($b/a$) as:

where $q_{0}$ is the intrinsic axial ratio of an edge-on galaxy. Following Catinella et al. (2012), we adopt $q_{0}$=0.2 for all galaxies and set to inclination of 90 degrees if $b/a<$0.2. Our conclusions are unchanged if we vary $q_{0}$ with morphology. The average $b/a$ of our sample is $\sim$0.5.

Stellar and gas velocity dispersions are defined as the linear average of the velocity dispersion measured in each ‘good’ spaxel (without any correction for inclination). We preferred linear to luminosity-weighted averages to be consistent with our velocity width measurements (which are not luminosity-weighted) and because these are less affected by beam smearing (Davies et al. 2011). Our conclusions, however, are unchanged if we use luminosity-weighted quantities. Excluding the effect of inclination, we assume an uncertainty of 0.1 dex in the estimate of both $V_{rot}$ and $\sigma$.

We combine dispersion and rotation through the $S_{K}$ parameter:

As discussed in Weiner et al. (2006) and Kassin et al. (2007), this quantity includes the dynamical support from both ordered and disordered motions and, thus, should be a better proxy for the global velocity of the galactic halo. Moreover, it is almost unaffected by beam smearing, as the artificial increase of $\sigma$ and decrease of $V_{rot}$ compensate each other once they are combined into $S_{K}$ (Covington et al. 2010).

Although the value of $K$ varies with the properties of the system, in this paper we follow the simple approach of Kassin et al. (2007) and Zaritsky et al. (2008), and fix $K$=0.5. Our conclusions do not change for 0.3$<K<$1.

The SAMI data are combined with multiwavelength observations obtained as part of the GAMA survey. Briefly, $r$-band effective radii, position angles and ellipticities are taken from the one-component Sersic fits presented in Kelvin et al. (2012)¹¹1We re-computed the ellipticity and position angle for seven galaxies with bright bars or other issues (GAMA 250277, 279818, 296685, 383259, 419632, 536625, 618152) as the published values do not match the orientation of the velocity field.. Stellar masses ($M_{*}$) are estimated from $g-i$ colours and $i$-band magnitudes following Taylor et al. (2011, see also ).

Visual morphological classification has been performed on the SDSS colour images, following the scheme used by Kelvin et al. (2014). Galaxies are first divided into late- and early-types according to their shape, presence of spiral arms and/or signs of star formation. Then, early-types with just a bulge are classified as ellipticals (E), whereas those with disks as S0s. Similarly, late-type galaxies with a bulge component are Sa-Sb, whereas bulge-less late-type galaxies are Sc or later.

Our $M_{*}$ vs. $V_{rot}$ relation has a larger scatter ($\sim$0.26 dex in $V_{rot}$ from the inverse fit)²²2All scatters in this paper are estimated from the inverse linear fit along the x-axis: i.e., we consider $M_{*}$ as independent variable. than classical Tully-Fisher relation ($\sim$0.08 dex). This is not surprising as our sample includes early-types and face-on systems that would normally be excluded from Tully-Fisher studies (e.g., Catinella et al. 2012). Indeed, a significant fraction of the scatter is due to spirals with bulges, and early types (see Fig. 2d).

The $M_{*}$ vs. $V_{rot}$ relation for the stars (circles) is significantly offset from the one of the gas (triangles): i.e., at fixed $M_{*}$, stars rotate slower than gas. This is clearer in Fig. 3a, where we compare $V_{rot}$ of gas and stars for the 62 galaxies with both measurements available. Once galaxies with clear misalignments between gas and stellar rotation axis are excluded (empty circles), we find that $V_{rot}$(gas) is, on average, $\sim$0.14 dex (with standard deviation $SD\sim$0.11 dex) higher than $V_{rot}$(stars). This is a consequence of asymmetric drift: while gas and stars experience the same galactic potential, a larger part of the stellar dynamical support comes from dispersion. The average ratio $V_{rot}$(stars)/$V_{rot}$(gas) is 0.75 ($SD\sim$0.20), roughly $\sim$20% lower than the value obtained by Martinsson et al. (2013) by comparing the maximum rotational velocities of pure disk galaxies ($V_{rot}$(stars)/$V_{rot}$(gas)$\sim$0.89). This is likely due to the fact that our sample is mainly composed by early-type spirals (see Fig. 1c) and that we probe only the central parts of galaxies, where asymmetric drift is more prominent.

For comparison, in Fig. 2a,d, we show the local stellar mass Tully-Fisher relation (Bell & de Jong 2001)³³3Stellar masses have been converted to a Chabrier Initial Mass Function following Gallazzi et al. (2008).. Our relation is flatter, showing a good match only at high $M_{*}$. This is because our rotational velocities are measured within $r_{e}$. As the rotation curves of giant galaxies rise more quickly than in dwarfs (Catinella et al. 2006), our $V_{rot}$ are close to the maximum rotational velocity only in massive systems (see also Fig. 2 in Yegorova & Salucci 2007).

As for the $M_{*}$ vs. $V_{rot}$ relation, the scatter of our $M_{*}$ vs. $\sigma$ relation is larger ($\sim$0.16 dex) than the one typically obtained for early-type galaxies only ($\sim$0.07 dex, Gallazzi et al. 2006). As Catinella et al. (2012), we find that the offset from the $M_{*}$ vs. $\sigma$(stars) relation for early-type galaxies (Gallazzi et al. 2006; dashed line) correlates with the concentration index. This confirms that, at fixed $M_{*}$, disks are more rotationally supported than bulge-dominated systems.

The scaling relations of stars and gas are offset, with $\sigma$(gas) on average 0.19 dex ($SD\sim$0.13 dex) lower than $\sigma$(stars) (Fig. 3b; see also Ho 2009). In addition, the $M_{*}$ vs. $\sigma$ relation for the gas is not linear, as galaxies with M${}_{*}<$10¹⁰ M_⊙ have roughly the same velocity dispersion ($\sim$30 km s^-1), i.e., the typical value observed in pure disk galaxies (Epinat et al. 2008).

The large scatter and the difference between stars and gas observed for the $M_{*}$ vs. $\sigma$ and $M_{*}$ vs. $V_{rot}$ relations disappear when $V_{rot}$ and $\sigma$ are combined in the $S_{0.5}$ parameter (see Fig. 2c,f). All morphological types follow the same scaling relation with just a few outliers. An inverse linear fit (assuming $S_{0.5}$ as dependent variable) gives a scatter of $\sim$0.1 dex (solid line in Fig. 2c,f)⁴⁴4Note that galaxies with both $S_{0.5}$(gas) and $S_{0.5}$(stars) do not contribute twice to the fit, as for these we use the average between the two values.. The slope and intercept of the linear relation (0.33$\pm$0.01, $-$1.41$\pm$0.08) are similar to what is found by Kassin et al. (2007) for star-forming galaxies at $z\sim$0.1 (dotted-dashed line). This is interesting, as they used maximum rotational velocities, instead of velocities within $r_{e}$.

The remarkable agreement between the $S_{0.5}$ for gas and stars is shown in Fig. 3c: the average logarithmic difference (gas-stars) is just $\sim-$0.02 dex ($SD\sim$ 0.07dex), even including disturbed galaxies. This is expected if both quantities trace the potential of the galaxy, and justifies their combination on the same scaling relation. The agreement between gas and stars is little affected by the value of $K$ used to combine $V_{rot}$ and $\sigma$. Indeed, the average logarithmic difference varies between $-$0.06 and +0.03 dex for 0.3$<K<$1, and $SD$ stays roughly the same. Fig. 3 confirms that the reduced scatter in the $M_{*}$ vs. $S_{0.5}$ relation is simply due to the fact that the combination of $V_{rot}$ and $\sigma$ provides a better proxy for the kinetic energy of a galaxy, which correlates with its mass.

Finally, we note that the $M_{*}$ vs. $S_{0.5}$ relation may become steeper for M${}_{*}<$10¹⁰ M_⊙. If we only fit massive galaxies (solid brown line in Fig. 2c,f, with its extrapolation indicated as dotted line), low-mass systems appear systematically below the relation. This non linearity likely reflects the one observed in the $M_{*}$ vs. $\sigma$ relation, but it is tempting to speculate whether this is also somehow related to the similar feature observed in the stellar mass Tully-Fisher relation (McGaugh et al. 2000), which disappears in its baryonic version, once the mass of cold gas is taken into account. Unfortunately, the absence of cold gas measurements makes it impossible to compute a baryonic $S_{0.5}$ relation. Thus, we conclude by simply noting that, if we use the ultraviolet and optical properties of our systems to predict their total gas content⁵⁵5Atomic hydrogen masses are estimated following Cortese et al. (2011). Total gas fractions are then obtained assuming a molecular-to-atomic gas ratio of 0.3 (Boselli et al. 2014) and a helium contribution of 30%., the residuals from the linear fit vary with gas fraction (Fig. 4) roughly as expected if the $S_{0.5}$ correlates linearly with total baryonic mass (red line in Fig. 4). However, given all the assumptions and uncertainties, the idea that a linear baryonic $S_{0.5}$ relation might be the physical relation linking galaxies of all types remains for now a speculation.