The slingshot effect as a probe of transverse motions of galaxies
  There are currently no reliable methods to measure transverse velocities of
galaxies. This is an important piece of information that could allow us to
probe the physics of structure formation as well as testing the underlying
theory of gravity. The slingshot effect, a special case of the Integrated
Sachs-Wolfe effect, is expected to create dipole signals in the temperature
fluctuations of the Cosmic Microwave Background Radiation (CMB). This effect
creates a hot spot behind and a cold spot in front of moving massive objects.
The dipole signal created by the slingshot effect can be used to measure
transverse velocities, but because the signal is expected to be weak, the
effect has not been measured yet. The aim is to show that the slingshot effect
can be measured by stacking the signals of galaxies falling into a collapsing
cluster. We evaluate if the effect can probe modified gravity. We use data from
a simulated galaxy catalogue (MDPL2) to mimic observations. We identify a
massive galaxy cluster, and make maps of the slingshot effect around infalling
galaxies. We add uncorrelated Gaussian noise to each map. The maps are rotated
according to the direction to the cluster centre, such that the dipole signal
will add up constructively when stacking. We compare each stack to a dipole
stencil and we find the probability for a false positive in the absence of the
slingshot signal. Each galaxy gives a signal of around $\Delta T/T \approx
10^{-9}$, while the precision of CMB experiments of today are $\Delta T/T
\approx 4 \times 10^{-6}$. By stacking around 10 000 galaxies, the slingshot
signal can be over the detectable threshold with experiments of today. However,
future CMB experiments must be used to be certain of the strength of the
observed signal.
