Boson stars from self-interacting dark matter
HJE
Boson stars from self-interacting dark matter
Joshua Eby 1 2 3
Chris Kouvaris 1 2
Niklas Gr nlund Nielsen 1 2
L.C.R. Wijewardhana 1 2 3
0 -Origins University of Southern Denmark
1 Campusvej 55 , DK-5230, Odense M , Denmark
2 Cincinnati , OH 45221 , U.S.A
3 University of Cincinnati, Dept. of Physics
We study the possibility that self-interacting bosonic dark matter forms starlike objects. We study both the case of attractive and repulsive self-interactions, and we focus particularly in the parameter phase space where self-interactions can solve well standing problems of the collisionless dark matter paradigm.
Cosmology of Theories beyond the SM; Classical Theories of Gravity
-
We
nd the mass radius
relations for these dark matter bosonic stars, their density pro le as well as the maximum
mass they can support.
1 Introduction 2 3
SIDM parameter space
2.1
DM scattering with boson stars
Bosonic dark matter
3.1
3.2
3.3
Non-interacting case
Repulsive interactions
Attractive interactions
4
Conclusions
drives the expansion of the universe in quintessence models [10].
These bosonic particles often make good Dark Matter (DM) candidates as well. One
reason for this is that unlike the Higgs, many of these new scalars would be stable or
longlived enough that they could coalesce into DM halos which constitute the seeds of galaxy
formation. Unlike the usual collisionless cold DM picture, however, we are interested in the
scenario where large collections of these bosons form bound states of macroscopic size due
to their self-gravitation (and self-interaction generically). For this picture to be consistent,
the scalars are taken to be su ciently cold so that they may coalesce into a Bose-Einstein
Condensate (BEC) state, and can thus be described by a single condensate wavefunction.
These wavefunctions can indeed encompass an astrophysically large volume of space and
have thus been termed \boson stars" [11].
It was shown many years ago that objects of this type are allowed by the equations of
motion, rst by Kaup [12] and subsequently by Ru ni and Bonazzola [13] in non-interacting
systems. They found a maximum mass for boson stars of the form Mmax
0:633MP2=m,
where MP = 1:22
1019 GeV is the Planck mass and m is the mass of the individual
bosons. (This is very di erent from the analogous limit for fermionic stars, termed the
Chandrasekhar limit, which scales as MP3=m2). Later, it was shown by Colpi et al. [11]
that self interactions in these systems can cause signi cant phenomenological changes. In
particular, they examined systems with repulsive self-interactions, and show that the upper
{ 1 {
limit on the mass is Mmax
MP3=m2, where
is a dimensionless 4 coupling.1 This
extra factor of MP=m as compared to the noninteracting case makes it more plausible
that boson stars can have masses even larger than a solar mass. A di erent method of
constraining the boson star parameter space, which ts the coupling strength using data
from galaxy and galaxy cluster sizes, has been considered in [14, 15].
The situation for attractive self-interactions is slightly more complex. The simplest
case involves a self-interaction of the form
4, where
< 0 for attractive interactions. If
this were the highest-order term in the potential, then it would not be bounded below, and
so one typically stabilizes it by the addition of a positive
6 term. We will assume that
the contribution of such higher-order terms is negligible phenomenologically (we address
the validity of that assumption in section 3.3). Furthermore, in this scenario the typical
sizes of gravitationally bound BEC states is signi cantly smaller than the repulsive or
noninteracting cases. This is because the only force supporting the condensate against collapse
comes from the uncertainty principle. Gravity and attractive self-interactions tend to shrink
the condensate. We will see in section 3 that the maximum mass for an attractive
condensate scales as Mmax
MP=p
j j. This result was originally derived using an approximate
analytical method [16], and was later con rmed by a precise numerical calculation [17].
DM self-interactions have already been proposed and studied in di erent contexts [18{
37]. One of the main reasons why DM self-interactions can play an important role is
due to the increasing tension between numerical simulations of collisionless cold DM and
astrophysical observations, the resolution of which (for the moment) is unknown. The rst
discrepancy, known as the \cusp-core problem", is related to the fact that dwarf galaxies
are observed to have
at density pro les in their central regions [38, 39], while N-body
simulations predict cuspy pro les for collisionless DM [40]. Second, the number of satellite
galaxies in the Milkly Way is far fewer than the number predicted in simulations [41{46].
Last is the so-called \too big to fail" problem: simulations predict dwarf galaxies in a mass
range that we have not observed, but which are too large to h (...truncated)