content_image/412738.jpg
<img src='content_image/412738.jpg'>

(such as halo II) are mostly in relatively low density re- gions in which scalar field has a light mass and the fifth force tends to saturate; this means that they should gen- erally have a higher internal density than the same halos in the ΛCDM simulation due to the enhanced growth by the fifth force. 

This above analysis is qualitatively confirmed by Fig. 9, where we can see that for the cases of µ = 10 − 6 (stronger chameleon) the difference between the predictions of the coupled scalar field models and the ΛCDM paradigm is really small for halo I. Furthermore, this figure also shows some new and more interesting features for the cases of µ = 10 − $^{5}$. Considering halo I in the models γ = 0 . 5 , µ = 10 − 5 and γ = 1 . 0 , µ = 10 − 5 for example: in the former case, the coupled scalar field model produces an obviously consistent higher internal density profile than ΛCDM, from the inner to the outer regions of the halo; while for the latter case, the density profile of the coupled scalar 

field model is lower in the inner region but higher in the outer region! 

We plan to make a detailed analysis of the complexities arising here regarding the effects of a coupled scalar field on the internal density profiles for halos in a future work, and in this work we will only give a brief explanation for the new feature observed above: Fig. 10 shows the dis- tributions of particle velocities and fifth-force-to-gravity ratio at the positions of the particles in halo I for the two models γ = 0 . 5 , µ = 10 − 5 and γ = 1 . 0 , µ = 10 − $^{5}$. As we can see there, for the model γ = 1 . 0 , µ = 10 − 5 the large value of γ makes the chameleon effect strong so that the fifth force is generally much smaller than gravity in mag- nitude, while at the same time the velocities of particles are more concentrated towards the high end, implying a significantly higher mean speed than ΛCDM (as we have checked numerically); as a result in the central region of the halo the particles have higher kinetic energy than in 

