The Shapes of the Rotation Curves of Star-forming Galaxies Over the Last $approx$10 Gyr. (arXiv:1811.05982v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Tiley_A/0/1/0/all/0/1">Alfred L. Tiley</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Swinbank_A/0/1/0/all/0/1">A. M. Swinbank</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Harrison_C/0/1/0/all/0/1">C. M. Harrison</a> (2), <a href="http://arxiv.org/find/astro-ph/1/au:+Smail_I/0/1/0/all/0/1">Ian Smail</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Turner_O/0/1/0/all/0/1">O. J. Turner</a> (3), <a href="http://arxiv.org/find/astro-ph/1/au:+Schaller_M/0/1/0/all/0/1">M. Schaller</a> (4,5), <a href="http://arxiv.org/find/astro-ph/1/au:+Stott_J/0/1/0/all/0/1">J. P. Stott</a> (6), <a href="http://arxiv.org/find/astro-ph/1/au:+Sobral_D/0/1/0/all/0/1">D. Sobral</a> (6), <a href="http://arxiv.org/find/astro-ph/1/au:+Theuns_T/0/1/0/all/0/1">T. Theuns</a> (4), <a href="http://arxiv.org/find/astro-ph/1/au:+Sharples_R/0/1/0/all/0/1">R. M. Sharples</a> (7,1), <a href="http://arxiv.org/find/astro-ph/1/au:+Gillman_S/0/1/0/all/0/1">S. Gillman</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Bower_R/0/1/0/all/0/1">R. G. Bower</a> (4,1), <a href="http://arxiv.org/find/astro-ph/1/au:+Bunker_A/0/1/0/all/0/1">A. J. Bunker</a> (8,9), <a href="http://arxiv.org/find/astro-ph/1/au:+Best_P/0/1/0/all/0/1">P. Best</a> (3), <a href="http://arxiv.org/find/astro-ph/1/au:+Richard_J/0/1/0/all/0/1">J. Richard</a> (10), <a href="http://arxiv.org/find/astro-ph/1/au:+Bacon_R/0/1/0/all/0/1">Roland Bacon</a> (10), <a href="http://arxiv.org/find/astro-ph/1/au:+Bureau_M/0/1/0/all/0/1">M. Bureau</a> (8), <a href="http://arxiv.org/find/astro-ph/1/au:+Cirasuolo_M/0/1/0/all/0/1">M. Cirasuolo</a> (2), <a href="http://arxiv.org/find/astro-ph/1/au:+Magdis_G/0/1/0/all/0/1">G. Magdis</a> (11,12) ((1) CEA, Durham, (2) ESO, (3) IfA, Edinburgh, (4) ICC, Durham, (5) Leiden, (6) Lancaster, (7) CfAI, Durham, (8) Oxford, (9) Kavli Institute, Japan, (10) Lyon, (11) Copenhagen, (12) IfA, Athens)

We analyse maps of the spatially-resolved nebular emission of $approx$1500
star-forming galaxies at $zapprox0.6$-$2.2$ from deep KMOS and MUSE
observations to measure the average shape of their rotation curves. We use
these to test claims for declining rotation curves at large radii in galaxies
at $zapprox1$-$2$ that have been interpreted as evidence for an absence of
dark matter. We show that the shape of the average rotation curves, and the
extent to which they decline beyond their peak velocities, depends upon the
normalisation prescription used to construct the average curve. Normalising in
size by the galaxy stellar disk-scale length ($R_{rm{d}}$), we construct
stacked position-velocity diagrams that trace the average galaxy rotation curve
out to $6R_{rm{d}}$ ($approx$13 kpc, on average). Combining these curves with
average HI rotation curves for local systems, we investigate how the shapes of
galaxy rotation curves evolve over $approx$10 Gyr. The average rotation curve
for galaxies binned in stellar mass, stellar surface mass density and/or
redshift is approximately flat, or continues to rise, out to at least
$6R_{rm{d}}$. We find a correlation between the outer slopes of galaxies’
rotation curves and their stellar mass surface densities, with the higher
surface density systems exhibiting flatter or less steeply rising rotation
curves. Drawing comparisons with hydrodynamical simulations, we show that the
average shapes of the rotation curves for our sample of massive, star-forming
galaxies at $zapprox0$-$2.2$ are consistent with those expected from
$Lambda$CDM theory and imply dark matter fractions within $6R_{rm{d}}$ of at
least $approx60$ percent.

We analyse maps of the spatially-resolved nebular emission of $approx$1500
star-forming galaxies at $zapprox0.6$-$2.2$ from deep KMOS and MUSE
observations to measure the average shape of their rotation curves. We use
these to test claims for declining rotation curves at large radii in galaxies
at $zapprox1$-$2$ that have been interpreted as evidence for an absence of
dark matter. We show that the shape of the average rotation curves, and the
extent to which they decline beyond their peak velocities, depends upon the
normalisation prescription used to construct the average curve. Normalising in
size by the galaxy stellar disk-scale length ($R_{rm{d}}$), we construct
stacked position-velocity diagrams that trace the average galaxy rotation curve
out to $6R_{rm{d}}$ ($approx$13 kpc, on average). Combining these curves with
average HI rotation curves for local systems, we investigate how the shapes of
galaxy rotation curves evolve over $approx$10 Gyr. The average rotation curve
for galaxies binned in stellar mass, stellar surface mass density and/or
redshift is approximately flat, or continues to rise, out to at least
$6R_{rm{d}}$. We find a correlation between the outer slopes of galaxies’
rotation curves and their stellar mass surface densities, with the higher
surface density systems exhibiting flatter or less steeply rising rotation
curves. Drawing comparisons with hydrodynamical simulations, we show that the
average shapes of the rotation curves for our sample of massive, star-forming
galaxies at $zapprox0$-$2.2$ are consistent with those expected from
$Lambda$CDM theory and imply dark matter fractions within $6R_{rm{d}}$ of at
least $approx60$ percent.

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