Astrophysical probes of the Vainshtein mechanism: Stars and galaxies

Ghost-free theories beyond the Horndeski class exhibit a partial breaking of the Vainshtein mechanism inside nonrelativistic sources of finite extent. We exploit this breaking to identify new and novel astrophysical probes of these theories. Nonrelativistic objects feel a gravitational force that is weaker than that predicted by general relativity. The new equation of hydrostatic equilibrium is derived and solved to predict the modified behavior of stars. It is found that main-sequence stars are dimmer and cooler than their general relativity counterparts but the red giant phase is largely indistinguishable. The rotation curves and lensing potential of Milky Way–like galaxies are calculated. The circular velocities are smaller than predicted by general relativity at fixed radius and the lensing mass is smaller than the dynamical mass. We discuss potential astrophysical probes of these theories and identify strong lensing as a particularly promising candidate.

Figure 1

The $n=3$ solutions of the Lane-Emden equation (black) and the MLE with $\mathrm{\Upsilon }=0.1$ (blue) and $\mathrm{\Upsilon }=0.2$ (red).

Figure 2

${\overline{\omega }}_R/{\omega }_R$ (red) and ${\overline{\xi }}_R/{\xi }_R$ (blue) as a function of $\mathrm{\Upsilon }$ for $n=3$ solutions of the MLE.

Figure 3

The luminosity enhancement for a $1M_{\odot }$ star as a function of $\mathrm{\Upsilon }$.

Figure 4

The luminosity enhancement as a function of mass for $\mathrm{\Upsilon }=0.3$ (red), $\mathrm{\Upsilon }=0.2$ (blue) and $\mathrm{\Upsilon }=0.1$ (green).

Figure 5

The HR diagram for a solar mass star. The red curve is the GR track when the metallicity is solar ($Z=0.02$) and the blue and green tracks show the evolution of the same star when $\mathrm{\Upsilon }=0.3$ and $\mathrm{\Upsilon }=0.1$ respectively. The black dashed (upper) and dotted (lower) lines show the tracks for the same star when the theory of gravity is GR and $Z=0.01$ and 0.03 respectively. The black circles indicate the point on the track when the age of the star is $4.6\times {10}^9\mathrm{yr}$. This is not shown for the $Z=0.01$ and 0.03 stars.

Figure 6

The HR diagram for a $2M_{\odot }$ star. The red curve is the GR track when the metallicity is solar ($Z=0.02$) and the blue and green tracks show the evolution of the same star when $\mathrm{\Upsilon }=0.3$ and $\mathrm{\Upsilon }=0.1$ respectively. The black dashed line shows the track for the same star when the theory of gravity is GR and $Z=0.03$.

Figure 7

The rotation curves for the NFW profile with $r_{\mathrm{s}}=20\mathrm{kPc}$ and ${\rho }_{\mathrm{s}}=6.68$. The GR prediction is shown in black and the red and blue curves correspond to $\mathrm{\Upsilon }=0.3$ and $\mathrm{\Upsilon }=0.5$ respectively.

Figure 8

The lensing potential predicted by the NFW profile with $r_{\mathrm{s}}=20\mathrm{kPc}$ and ${\rho }_{\mathrm{s}}=6.68$. The GR prediction for this ratio is unity. The ${\mathrm{G}}^3$-Galileon predictions with $\mathrm{\Upsilon }=0.1$, $\mathrm{\Upsilon }=0.3$ and $\mathrm{\Upsilon }=0.5$ are plotted using black, red and blue curves respectively.