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Dark Matter as a Possible New Energy Source for Future Rocket Technology

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Current rocket technology can not send the spaceship very far, because the amount of the chemical fuel it can take is limited. We try to use dark matter (DM) as fuel to solve this problem. In this work, we give an example of DM engine using dark matter annihilation products as propulsion. The acceleration is proportional to the velocity, which makes the velocity increase exponentially with time in non-relativistic region. The important points for the acceleration are how dense is the DM density and how large is the saturation region. The parameters of the spaceship may also have great influence on the results. We show that the (sub)halos can accelerate the spaceship to velocity $ 10^{- 5} c \sim 10^{- 3} c$. Moreover, in case there is a central black hole in the halo, like the galactic center, the radius of the dense spike can be large enough to accelerate the spaceship close to the speed of light. Comment: 7 pages, 6 figures; v2, minor correction, add the discussion in annihilation speed
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arXiv:0908.1429v2 [astro-ph.CO] 9 Oct 2009
Dark Matter as a Possible New Energy Source for Future Rocket Technology
Jia Liu
Center for Cosmology and Particle Physics, Department of Physics,
New York University, New York, NY 10003, USA
Institute of Theoretical Physics, School of Physics, Peking University, Beijing 100871, P.R. China
(Dated: May 23, 2018)
Current rocket technology can not send the spaceship very far, because the amount of the chemical
fuel it can take is limited. We try to use dark matter (DM) as fuel to solve this problem. In this
work, we give an example of DM engine using dark matter annihilation products as propulsion. The
acceleration is proportional to the velocity, which makes the velocity increase exponentially with
time in non-relativistic region. The important points for the acceleration are how dense is the DM
density and how large is the saturation region. The parameters of the spaceship may also have
great influence on the results. We show that the (sub)halos can accelerate the spaceship to velocity
105c103c. Moreover, in case there is a central black hole in the halo, like the galactic center,
the radius of the dense spike can be large enough to accelerate the spaceship close to the speed of
light.
PACS numbers: 95.35.+d, 45.40.Gj, 89.30.-g
I. INTRODUCTION
It is difficult for human to reach the stars using current rocket technology. The energy sources range from chemical
fuel, nuclear power and even anti-matter conceptually. The major problem in these systems is that propulsion required
large amount of time and fuel[1]. We try to solve this problem by starting at the requirement of large amount of
fuel. We all know that current rockets in function are chemical rockets which take oxidant and fuel at the same time.
Interestingly, the airplanes with similar propulsion system only take fuel, without oxidant, because in the atmosphere
there are enough oxygen which are absorbed by airplane engines during the flight. Similarly, if there are enough fuel
in the universe, the spaceship may absorb them during its flight like airplanes absorb the oxygen. Fortunately, dark
matter is widely spread in the universe and the mass density is about five times of the baryonic matter density[2],
which make it a possible new energy source for interstellar flight. Thus the requirement of fuel may be solved in the
self-help way with dark matter as the energy source.
II. DM ENGINE AND ACCELERATION IN THE SATURATION DENSITY
We give an example of DM engine which uses DM annihilation remnants as propulsion. Fig.1 is a sketch of the DM
engine for this kind of new spaceship. The DM engine is the box in the picture. Here we assume the DM particle and
the annihilation products can not pass through the wall of the box. In picture A, the space ship moves very fast from
right to left. The DM particles, which are assumed to be static, go into the box and are absorbed in the picture B.
In the picture C, we compress the box and raise the number density of the DM for annihilation, where we assume the
annihilation process happens immediately. In the picture D, only the wall on the right side is open. The annihilation
products, for example Standard Model (SM) particles, are all going to the right direction. The processes from A to
D are the working cycle for the engine. Thus, the spaceship is boosted by the recoil of these SM particles. Note the
spaceship can decelerate by the same system when it reaches the destination, by opening the left wall in the picture
D.
This kind of new spaceship has a very interesting character that the faster it is, the easier it accelerates. In the
picture A, we assume the rest mass of the spaceship is Mand its velocity is βin the unit of speed of light. The time
for one cycle of the engine is dt and the area of the engine is S. During one work cycle, the number of DM particles
collected by the engine is N=βdt·S·ρD
mD, where ρDand mDare the density of DM and mass of DM, respectively. In
picture D, we assume there are only one kind of particles X as the annihilation products for simplicity. The annihilation
process is DD X¯
X, with the mass mX< mD. For the DM particles, we assume DM mass mDO(100GeV ) and
Electronic address: jl3473@nyu.edu
2
A
DM
B
DM
C
DM
D
'
SM particles
FIG. 1: The illustration of work cycle for the DM engine.
the annihilation products to be SM fermions mainly, which are quite natural in SuperSymmetry and Extra Dimension
models. Thus, the mass of the annihilation products mXare quite small comparing with the mass of dark matter
mD. So it is reasonable to use the approximation mX= 0, where products are treated as massless photon in the
following calculation. Using the conservation of energy and momentum, we can get
βdt ·S·ρD+p0=p0+dp0+ε
0 + p1=p1+dp1ε·θ(1)
where p0=Mγ and p1=M γβ are the energy and the momentum of the spaceship, and γ(1 β2)1/2,εis
the energy of the massless photons. θis defined as the propulsion efficiency, which means θ[0,1]. For example, if
the annihilation particles all go to the right direction, then θ= 1. However, if the annihilation particles have equal
possibility go into any direction in the right hemisphere, then θ= 1/2. Moreover, it can also be used to count in the
other inefficiency of the engine. By the Eqn.1, one can get the differential equation for the velocity,
θ1+β=γ3
dt (2)
where kD/M . In the non-relativistic region, the above equation has the simple form,
θk ·β=
dt .(3)
To carry out the numerical calculations, we give some reasonable parameters first. We assume the weight of the
spaceship is M= 100ton and the area is S= 100m2, according to the current rockets and space shuttles. For the
DM density, we use the saturation density in the center of cusped halos ρsat . The saturation density in the halo is
due to the balance between the annihilation rate of the DM [hσviρsat /mD]1and the gravitational in falling rate
3
of the DM (G¯ρ)1/2, where the ¯ρis taken to be 200 times of the critical density. Thus the saturation density is
ρsat 1019M·kpc3[3, 4]. The propulsion efficiency is taken to be θ= 0.5, since in the picture D we assume the
annihilation particles have equal possibility go into any direction in the right hemisphere. We can also rewrite the
parameter kas following,
k= 2 ×104s1·ρ
1019M·kpc3
S
100m2
100ton
M(4)
One can solve the Eqn.2 and get the time and length needed for acceleration as the function of velocity,
t= (θk)1·[1 + θβ
p1β2+In(β
1 + p1β2)]
β
β0
,(5)
L= (θk)1·β+θ
p1β2
β
β0
.(6)
where β0is the initial velocity at the t= 0. We give the plots of the above equations in Fig.2. We can see the
velocity increases exponentially with time, since the acceleration is proportional to the velocity. In the non-relativistic
region, where β1, the Eqn.5 and the Eqn.6 can be simplified as
β=β0eθkt,(7)
L= (θk)1(ββ0).(8)
The initial velocity β0is taken to be 106cwhich is much smaller than the first cosmic velocity. However, the result
is not sensitive to the initial velocity, because of the exponential increase. In Fig.2, we see the spaceship can reach the
relativistic speed in about 2 days and the length needed for acceleration is about 104pc. From the above equations,
if the DM density ρand the area of the spaceship Sare larger, the time tand length Lneeded for acceleration will go
down. If the mass of spaceship Mis larger, the time tand length Lneeded for acceleration will increase. However,
the mass of DM particle does not have great influence on results, but the DM density does.
FIG. 2: The velocity as a function of the time and length needed for the acceleration in the saturation density.
4
III. ACCELERATION IN THE HALO OR SUBHALO
Before celebration for the reach of relativistic speed, we should check whether the saturation region in the halo or sub-
halo is large enough for the above calculation. The DM profile can be parameterized as ρ(r) = ρs
(r/rs)γ[1+(r/rs)α](βγ),
where ρsand rsare the scale density and scale radius parameters respectively. The parameters (α, β, γ ) are (1,3,1)
for NFW profile[5]. Since we are interested in the central region of halo, where rrs, the profile can be simplified
as,
ρ=ρsrs
r.(9)
This profile is singular at the center of the halo. It is natural to have cut-off for this singularity due to the balance
between the annihilation rate of the DM and the gravitational in falling rate of the DM. The saturation DM density
is taken to be ρsat 1019 M·kpc3, thus the radius of saturation is rsat =ρsrs/ρsat. Once we know the scale
density ρsand scale radius rs, we can calculate the saturation radius rsat. The ρsand rscan be fully determined by
the concentration model and DM halo mass, which will be calculated in the appendix. Here we show the saturation
radius rsat in Fig.3. We can see the saturation radius of halo or subhalo is much smaller than the required length for
acceleration to the relativistic speed.
FIG. 3: The saturation radius rsat for different (sub)halo mass and concentration models. The B01 and ENS01 stand for
different concentration models which are described in the appendix.
In Fig.4, we show the details of acceleration in the subhalo. The subhalo with mass 106Min B01 model is taken
as an example, which has saturation radius of about 109pc. Starting from the center of subhalo with initial velocity
β0= 106c, it reaches the velocity of about 105cwhen it leaves the saturation region, which can be read out from
the Fig.2. However, the rest of the subhalo is not sufficient to accelerate the spaceship to the relativistic speed, since
the density begins to decrease by r1. By solving the differential equation numerically, we can get the relations among
velocity, time and distance in Fig.4. We can see the spaceship reaches the velocity 104cin about ten days. However,
its velocity hardly increases after that, since the DM density goes down quickly. We can see that the acceleration is
fastest in the saturation area of the halo. But the rest region of subhalo can still accelerate the spaceship from the
velocity 105cto the velocity 104c.
To better understand the acceleration power of the (sub)halos, we give the velocity at different times for different
(sub)halos mass and spaceship parameters in Fig.5. From the picture on the left, we can find that the subhalos have
the power to accelerate the spaceship to velocity 105c103cwith reasonable parameters S/M = 100m2/100ton. In
the first few hours, the spaceship flies in the saturation region where they will be accelerated to velocity 106c104c,
which can be understood with the help of Fig.2 and Fig.3. Out of the saturation region, the velocity of the spaceship
can get further boosted by about one order in the r1density region. Note that the above accelerations take place
at the very center of halo, which is far less than the scale radius rs. The above results rely on the parameters of
spaceship, e.g. the ratio S/M. If we lower the the weight of spaceship and increase the area of the engine, the velocity
we can achieve will significantly increase. We specially give the plot on the right for S/M which is ten times larger,
although the parameters maybe unreasonable in practice. It shows the the corresponding velocity increases about ten
times. The main reason is the velocity at r=rsat increases by ten times, which can be understood with the Eqn.8.
5
FIG. 4: The velocity as a function of the time and length needed for the acceleration in the DM (sub)halo. The spaceship
starts from the (sub)halo center with initial velocity β0= 106c.
FIG. 5: The velocity at time t= 1day and t= 1month for different (sub)halos mass and spaceship parameters. The concen-
tration model is taken to be B01. The spaceship is still assumed to be started at the center of (sub)halo with initial velocity
β0= 106c.
Anyway, the (sub)halos seem difficult to boost the spaceship to relativistic velocity, because their saturation radius
is small comparing with the required acceleration length 104pc in the Fig.2. In the above calculation, we assume
there are no baryonic matter in the halo. The gravity from the DM halo have negligible effects on the spaceship, even
at the saturation region. Note the saturation density ρsat 1019 M·kpc3is much smaller than the density of water
1g/cm31031 M·kpc3.
However, in case there are baryonic matter in the halo, it may modify the DM profile. The adiabatic contraction
due to dissipating baryons can steepen the DM profile[6]. A more interesting case is that there is a central black hole
in the DM halo, for example at galactic center. The DM density can become a dense spike due to accretion by the
black hole, assuming adiabatic growth of the black hole[7]. The annihilations in the inner regions of the spike set a
maximal dark matter density ρcore =mD
hσvitbh 1017M·kpc3, where mDis the mass of DM particle, and tbh is the
age of black hole, conservatively 1010yr. And more importantly, the radius of the core can be as large as O(102pc)
for inner cusped model like NFW profile. Recall the Eqn.6, the required acceleration length for velocity 0.9cis about
O(102pc) in this case, which means the spaceship can achieve the velocity close to the speed of light.
6
IV. CONCLUSION AND DISCUSSIONS
In this work, we give an example of DM engine using DM annihilation products as propulsion. The acceleration is
proportional to the velocity, which makes the velocity increase exponentially with time in the non-relativistic region.
The important points for the acceleration are how dense is the DM density and how large is the saturation region.
The parameters of the spaceship also have great influence on the results. For example, the velocity will increase
if S/M increases. We show that the (sub)halos can accelerate the spaceship to velocity 105c103cunder the
reasonable parameters of spaceship. Moreover, in case there is a central black hole in the halo, like galactic center,
the core radius of DM can be large enough to accelerate the spaceship close to the speed of light.
We have used three assumptions in this work. First, we have assumed static DM for simplicity. But the DM
particle may have velocity as large as O(103c). Once we know the velocity distribution of DM, it can be solved by
programming the direction of the spaceship when speed is low. An analogue in our daily life is airplanes work well
in both headwind and tailwind. Second, we have assumed the DM particles and the annihilation products can not
pass through the wall of the engine. For the annihilation products, they may be SM fermions which have electric
charges. Thus we can make them go into certain direction by the electromagnetic force. The most serious problem
comes from DM which are weakly interacting with matter. Current direct searches of DM have given stringent bound
on cross-section of DM and matter. It may be difficult using matter to build the containers for the DM, because
the cross-section is very small. However, the dark sector may be as complex as our baryon world, for example the
mirror world. Thus the material from dark sector may build the container, since the interactions between particles
in dark sector can be large. Third, the annihilation process is assumed to happen immediately in the picture C. This
is the second serious problem we should pay attention to. The annihilation speed takes the form, A=hσviρ2
sat
2m2
D.
The hσviis taken to be the natural scale of the correct thermal relic, which is 3 ×1026cm3s1. One can show that
A= 2.2×107cm3s1. However, the number density of the dark matter is nD=ρsat
mD= 4 ×109cm3. Thus,
to make the annihilation process efficient, we have to compress the volume of the engine to raise the annihilation
speed. Whether it can be achieved in the future is not clear. Nevertheless, the engine works in the vacuum where the
baryonic matter is dilute, which means we do not need to worry about the pressure from the baryonic matter.
Sometimes, when looking at the N-body simulation pictures of DM, I think it may describe the future human
transportation in some sense. In the picture, there are bright big points which stand for large dense halos, and the
dim small points for small sparse halos. Interestingly, these halos have some common features with the cities on
the Earth. The dense halos can accelerate the spaceship to higher speed which make it the important nodes for the
transportation. However, the sparse halos can not accelerate the spaceship to very high speed, so the spaceship there
would better go to the nearby dense halo to get higher speed if its destination is quite far from the sparse halos.
Similarly, if we want to take international flight, we should go to the nearby big cities. The small cities usually only
have flights to the nearby big cities, but no international flights. Thus we can understand the dense halos may be
very important nodes in the future transportation, like the big cities on the Earth.
APPENDIX: DARK MATTER HALO AND SUBHALO PROFILES
Based on N-body simulations, the DM distribution can usually be parameterized as,
ρ(r) = ρs
(r/rs)γ[1 + (r/rs)α](βγ),(A.1)
where ρsand rsare the scale density and the scale radius parameters respectively. The parameters (α, β , γ) are
(1,3,1) for NFW profile. In this appendix, we briefly introduce how rsand ρsare calculated. The two parameters
can be determined once we know the (sub)halo mass Mvand the concentration parameter cvwhich depends on the
specific concentration model. The calculations are following the method in Ref.[4]. In the appendix of Ref.[8], we
have shown how to determine the rsin detail.
For the NFW profile, the scale radius rsis
rnfw
s=rv(Mv)
cv(Mv).(A.2)
where rvis the virial radius of the subhalo which is often approximated as the radius within which the average
density is greater, by a specific factor ∆ = 200, than the critical density of the Universe ρc= 139Mkpc3(M
is mass of the Sun). Thus rvcan be expressed as rv=Mv
(4π/3)∆ρc1/3. The cvis the concentration parameter of
7
the subhalo which is determined by the subhalo mass Mvand concentration model. We use the same method as
Ref.[4] which adopts two concentration models, which are ENS01[9] and B01[10]. In the Ref.[4], the cvis fitted in a
polynomial form as
ln(cv) =
4
X
i=0
Ci×ln Mv
Mi
,(A.3)
where Ci={3.14,0.018,4.06×104,0,0}and {4.34,0.0384,3.91×104,2.2×106,5.5×107}for ENS01
and B01 model respectively.
The density scale ρscan be determined by the mass relation Rρs(r)dV=Mv. One can get the scale density ρs,
ρnfw
s=Mv/[4πr3
sA(cv)],(A.4)
where A(cv)In(1 + cv)cv/(1 + cv). In Fig.6, the scale radius rsand the scale density ρsare plotted as a
function of subhalo mass Mvto show how large and how dense the subhalos are. We can see the scale radius rsis
quite large which shows the acceleration is mostly done in the rrsregion of the (sub)halo.
FIG. 6: The scale radius rsand the scale density ρsas a function of (sub)halo mass Mv. This plot assumes the (sub)halos
have NFW profile.
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... Experiments to discover this matter are conducted at the LHC proton accelerator at the European Organization for Nuclear Research (Switzerland). The potential for using dark matter as an energy source for spacecraft on long missions is being discussed [Liu, 2009]. If relevant hypotheses are confirmed, a unit of dark matter mass could emit 5 billion times more energy than a mass unit of dynamite [Casalino et al., 2018]. ...
Article
Full-text available
The introductory article to the special issue “The Future of Energy” is devoted to promising areas of development of the global energy complex, the assessment of their contribution to overcoming global challenges, and ensuring sustainable development. The trends under consideration differ significantly in the rate of evolution. Prospective development trajectories present both opportunities and risks specific to the fuel and energy complex of a particular country. Success in using emerging advantages and leveling threats depends upon a combination of internal and external factors, including the choice of public policy measures and the effectiveness of their implementation.
... Experiments to discover this matter are conducted at the LHC proton accelerator at the European Organization for Nuclear Research (Switzerland). The potential for using dark matter as an energy source for spacecraft on long missions is being discussed [Liu, 2009]. If relevant hypotheses are confirmed, a unit of dark matter mass could emit 5 billion times more energy than a mass unit of dynamite [Casalino et al., 2018]. ...
Article
Full-text available
The introductory article to the special issue “The Future of Energy” is devoted to promising areas of development of the global energy complex, the assessment of their contribution to overcoming global challenges, and ensuring sustainable development. The trends under consideration differ significantly in the rate of evolution. Prospective development trajectories present both opportunities and risks specific to the fuel and energy complex of a particular country. Success in using emerging advantages and leveling threats depends upon a combination of internal and external factors, including the choice of public policy measures and the effectiveness of their implementation. © 2018, National Research University, Higher School of Econoimics. All rights reserved.
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J. S. Bullock et al., Mon. Not. Roy. Astron. Soc. 321, 559 (2001) [arXiv:astro-ph/9908159].
Rocket Scientists Say We'll Never Reach the Stars
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  • Q Yuan
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