Balance of Dark and Luminous Mass in Rotating Galaxies

A fine balance between dark and baryonic mass is observed in spiral galaxies. As the contribution of the baryons to the total rotation velocity increases, the contribution of the dark matter decreases by a compensating amount. This poses a fine-tuning problem for $\Lambda \mathrm{CDM}$ galaxy formation models, and may point to new physics for dark matter particles or even a modification of gravity.

Figure 1

The rotation curves of two galaxies, NGC 2403 and UGC 128, of similar mass but very different size. The contributions of the baryonic components (stars plus gas: solid lines) are very different even though the dark matter halos (dashed lines) are similar. Lines for the baryons and dark halo of NGC 2403 end with its velocity data at 20 kpc while those of UGC 128 continue to 40 kpc. Arrows mark the radius $R_p$ where the peak of the baryonic rotation occurs.

Figure 2

Correlations of various galaxy properties with baryonic mass. Mass is measured in solar masses, velocities in $\mathrm{km}{\mathrm{s}}^{-1}$, and radii in kpc. Top left: the observed velocity $V_p$ at $R_p$. Top right: the velocity $V_b$ due to the baryons at $R_p$. Bottom left: the scale length of the stellar disk $R_d$. Bottom right: the radius $R_p$ where the baryons contribute maximally to the rotation. The solid lines are the fits to the data given in Table . For comparison, the fits to the other velocity is shown as a dashed line in the top panels.

Figure 3

Velocity residuals from the luminosity-$V_p$ relation (top) and the ${\mathcal{M}}_b\mathrm{\text{−}}{V}_p$ relation (bottom) as a function of scale length residuals. In the top panel, open circles are $B$-band data and filled circles are $K^{\prime }$-band data. Fits to these residuals (dotted lines) have slopes close to zero (solid lines). The mass residuals do not show the slope expected for pure disks (dashed line).

Figure 4

The fractional contribution to the total velocity at the peak radius by baryons ($V_b/V_p$) and dark matter ($V_h/V_p$). These correlate with baryonic surface density, determined either from the $K^{\prime }$-band light [19] and stellar population models [26] (top) or Eq. (3) (bottom). Disks come closer to being maximal as surface density increases. Curiously, the dark matter contribution declines in compensation, maintaining a seesaw balance with the baryons.