Issue |
A&A
Volume 510, February 2010
|
|
---|---|---|
Article Number | L3 | |
Number of page(s) | 6 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/200913597 | |
Published online | 10 February 2010 |
Online Material
Appendix A: Note on the influence of both the Riemann solver and the numerical resolution
![]() |
Figure A.1:
Case |
Open with DEXTER |
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Figure A.2:
Density and temperature maps in the equatorial plane at time t=38.3 kyr (
|
Open with DEXTER |













Figure A.1 portrays the density maps in the equatorial plane for the 4 calculations, at time
.
The calculations performed with the LF solver,
and
clearly diverge from the others, since it fragments. The lack
ofresolution clearly induces inaccurate fragmentation. The three other
calculations are qualitatively similar (no fragmentation) and agree
with Hennebelle & Teyssier (2008)
results (obtained using a Roe-type Riemann solver). This indicates that
the numerical resolution should be enhanced with the LF solver to avoid
spurious effects caused by the diffusivity of the solver. We note that
these differences are more important in the case of FLD calculations,
since depending on the strength of the magnetic braking, radiative
transfer can have two opposite effects. If magnetic braking is
insignificant (with poor resolution and a diffuse Riemann solver), the
material at the centrifugal barrier cools and then fragments. On the
other hand, when the magnetic braking is efficient (with HLLD or a high
resolution), the infall velocity and consequently, the accretion
luminosity, become higher, which prevents fragmentation occurring (as
material loses angular momentum and heats up).
Appendix B: Case
= 1000
For this quasi-hydro case, the initial dense core is highly
gravitationally unstable. We performed three types of calculations with
the LF Riemann solver: one with the barotropic EOS and
,
and two with the FLD and different adiabatic exponents (
and
). The value
is more appropriate for T> 100 K, when the rotational degrees of freedom of H2 are excited
(e.g., Machida et al. 2008). Using
yields cooler adiabatic cores than with
at the same density. Higher densities and temperatures in the core are thus reached more rapidly.
Figure A.2 portrays density and temperature maps in the equatorial plane for the three aforementioned calculations at a time t=1.15
.
Temperature maps range from 11.4 K to 20 K. As pointed out in Commerçon et al. (2008),
the horizon of predictability is very short when the initial thermal
support is low. Calculations do not show a convergence to the same
fragmentation pattern, since we do not integrate the same system
equations. The FLD calculations yield different fragmentation modes for
the two values of
's: for
,
we obtain a central object and two satellites (4 at later times), whereas for
,
we obtain a ring fragmentation pattern with orbiting fragments linked
by a bar. The barotropic EOS calculation does not produce a central
object.
From the temperature map of the FLD case with
,
we see that the central region is quite hot. Fragments are compressed more and radiate more energy than for
.
Fragments also form more rapidly than the time required for the
radiative feedback to become significant (at beginning of the second
collapse).
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