Environmental Engineering Reference
In-Depth Information
Ta b l e 1
Collision models and detected accretion centers
Model
log
10
ˁ
max
ˁ
0
V
app
c
0
t
max
t
ff
R
c
N
acc
Np
acc
M
av
/
M
10
−
6
P1
R
0
/
4
2.5
7.62
0.44
30
6
6
.
24
×
10
−
6
P2
R
0
/
4
5.0
7.78
0.48
43
5
4
.
39
×
10
−
6
P3
R
0
/
4
10.0
7.89
0.51
26
6
5
.
61
×
10
−
6
P4
R
0
/
2
2.5
6.30
0.26
37
5
4
.
07
×
10
−
6
P5
R
0
/
2
5.0
7.90
0.26
26
7
5
.
62
×
P6
R
0
/
2
10.0
2.26
0.35
-
-
-
10
−
18
g
cm
3
10
11
s,
The density and time are normalized by
ˁ
=
9
.
2
×
/
and
t
ff
=
6
.
925
×
0
respectively
speed. As a way of comparing our simulations with other simulations elsewhere, in
the fourth and fifth columns we show the peak density
ˁ
max
reached in each run and
the evolution time, respectively. In the sixth column we show the number
N
acc
of
accretion centers found for each system. In the seventh column we show the average
number of
SPH
particles
Np
acc
per accretion center formed in each model while in
the eight column we show the accretion center average mass
M
av
/
M
sun
.
3 The Computational Method
We carry out the time evolution of the initial distribution of particles with the fully
parallel
Gadget
2 code, which is described in detail by Springel (
2005
).
Gadget
2
is based on the
treePM
method for computing the gravitational forces and on the
standard
SPH
method for solving the Euler equations of hydrodynamics.
Gadget
2
incorporates the following standard features: (i) each particle
i
has its own smoothing
length
h
i
; (ii) particles are also allowed to have individual gravitational softening
lengths
ʵ
i
, whose values are adjusted such that for every time step
ʵ
i
h
i
is of order
unity.
Gadget
2fixesthevalueof
ʵ
i
for each time-step using the minimum value of
the smoothing length of all particles, that is, if
h
min
=
min
(
h
i
)
for
i
=
1
,
2
...
N
, then
ʵ
i
h
min
.
The
Gadget
2 code has an implementation of aMonaghan-Balsara formfor the arti-
ficial viscosity, see Monaghan and Gingold (
1983
), and Balsara (
1995
). The strength
of the viscosity is regulated by setting the parameter
=
3
2
ʱ
ʽ
=
0
.
75 and
ʲ
ʽ
=
×
ʱ
ʽ
,
see Eq. (14) in Springel (
2005
). We here fix the Courant factor to 0
1.
Let us now briefly describe the modifications implemented into the
Gadget
2 code
for detecting accretion centers. Any gas particle with density higher than
.
ˁ
s
is a
candidate to be an accretion center. We localize all candidate particles for a given
time
t
. We then test the separation between candidates: if there is one candidate
with no other candidate closer than 10
r
acc
, then this particle is identified as an
accretion center at time
t
. We define
r
acc
as the neighbor radius for an accretion
center, given by
r
acc
×
=
1
.
5
×
h
min
. In this way
r
acc
determines a set of particles
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