alx-ai/arxiv_papers · Datasets at Hugging Face

text stringlengths 0 44.4k
thickness is roughly
Δ=VAl2
2νniVS
Δ is the lengthsca le over which dissipation occurs, and the smaller Δ is the hotter the gas
becomes. If grains were present and well- coupled to the magne tic field, the expression for Δ
would contain the sum of νni and νng , rather than νni alone. However , collisions tend to
decouple the grains from the magne tic field, an effect considered by Draine [22] and Draine,
Rober ge and Dalgarno [23] whose models of perpendicul ar shocks are reliab le for cases in
which the preshock value of nH is ≤ 106 cm-3.
8At higher densit ies a self consisten t calcul ation of the average charge on the grains and the
fraction al ioniz ation is required to obtain accurat e results for νni and for the effect that grains
have on the shock structure. Pilipp, Hartquist and Havnes [24] includ ed such a calculation in
each of their models of perpendi cular shocks. They also includ ed fluid equations for the
grains rather than adop t a simpl er approxi mation to calculate the effects of dust [22, 23]. This
led them to discover a run-away proces s operat ing in perpend icular shocks for which the
preshock value of nH is 107 cm-3 or highe r. At such densities, the ratio of n(e)/\|Zg\|ng drops
below unity within the precursors of sufficiently fast shocks. n(e) is the electron number
density , \|Zg\|e is the magni tude of the average charge carried by grains and ng is the number
density of grains. Once this ratio drops below unity , \|Zg\| begins to drop as there are
insuf ficien t electrons to continue charging the grains. Assume that the shock propagates in
the x-direc tion and the magnet ic field is in the y-direct ion and that Ω/νgn , the grain Hall
parame ter, is small. Then the grains separate from the other charged particles sufficien tly to
generat e an x-compon ent of the ele ctric field with a magnitud e given approxima tely by

Ex=mgνgn∣vnx−vgx∣
∣Zg∣e
Here mg is the mass of a grain. This creat es an ion drift veloc ity componen t in the z-direc tion
with a magn itude of cEx/By . As \|Zg\| drops, this component of the drift velocity increases.
This causes an incre ase in the rate at which a grain exper iences collisions with ions, which
leads to a further drop in \|Zg\|. Hence, a runaway occurs.
The recent work of Guill et, Jones and Pineau des Forêts [25, 26] represents a signif icant
developm ent in the modeling of perpendicu lar shocks in dusty star forming regions. In their
work on C-typ e shocks [25], they adopt ed a hybrid approach. The gaseous species were
described as fluids, whereas the trajectories and charges of many individua l dust particles
were followed. The treatmen t gave self-consistent results for the grain charges, gas phase ion
9and electron abundan ces and dynam ics. Though the fluid approach of Pilipp et al. [24] is
valid for a wide range of parame ter space, the Guille t et al. [25] method is required in cases
in which dust gyroradi i are comparab le to or larger than the scales on which variations of
parame ters vary in shocks.
6. Steady-S tate Models of Oblique Shock s.
Pilipp and Hartquist [27] adopt ed a fluid description of grain dynami cs in studies of steady
shocks propagat ing obliquely to the upstrea m magnet ic field in dusty star forming regions.
We will assume that a shock propagates in the x-dire ction and that the upstream magn etic
field has x and y componen ts but its z component is zero. They found that grain-neutr al
collisions lead to a rotation of the magneti c field in a C-type shock precursor around the x-
direct ion.
The following considera tions show why such rotation occurs. In the shock frame the z-
component of the electr ic field, Ez , is VSBy0/c , where By0 is the y-componen t of the upstream
magnet ic field. Thus, there is a componen t of ExB drift in the x-dire ction. In the absenc e of
collisions, the x-compon ents of the ExB drift velocities of all species are equal. However ,
grain-neutr al collisions are signific ant leading to a non-zero x-component of the Hall current.
For a steady shock, the equa tion of charge conserva tion requires that the x-component of the
total current is zero. Thus, a current parallel to the magneti c field having a x-componen t that
cance ls the Hall current component in the x direc tion must exist. Use of Ampere ’s Law sho ws
that the curren t along the magnet ic field gener ates a component of the magne tic field in the z
direct ion.
By integrat ing from an upstrea m point in the downstrea m direct ion, Pilipp and Hartquist [27]
succeeded in finding only intermedi ate-mode shock solutions. Such solutions are
inadm issible [28].
10Wardle [29] showed that integra tion in the downstrea m direc tion will not yield steady fast-
mode solut ions because the down stream state corresponds to a saddle point. He found fast-
mode solut ions by integra ting upstream from the downstream state.
Chapman and Wardle [30] have extended this work and shown that the inclusion of PAHs
leads to a drop in the gas phase electron abundance and enhanc ed rotation of the magn etic
field. PAHs are nano-part icles thought to be abundant in clouds more diffuse than star
forming regions. As mentioned earlier, in such regions desorpt ion of material from the gas
phase may result in a ll part icles gro wing to sizes close to 0.1 μm.
Integrat ion in the upstream direc tion is not appropri ate if condi tions anywhere in a shock
deviat e from equilibr ium. After shocked gas has cooled, the abundanc e of H2O, an impor tant
coolant in shocked dense core mater ial, remains far from its equil ibrium value for many times
the flow t ime through a shock. Other che mical species also have abundances that are far from
their equilibr ium values for considerab le periods. Consequen tly, the calcula tion of shock
structures by integrat ion in the upstream direc tion is inappropr iate, and the use of a time-
dependent, rather than a steady-state, approa ch is necessary to overcome the difficulties found
by Pilipp and Hartquist [27] and explain ed by Wardle [29]. Falle [31] has deve loped an
appropriat e time-depend ent approach.
7. Time-Depen dent Mode ls of Oblique Shock s in Dusty R egions.
Van Loo et al. [32] have used the techn ique deve loped by Falle [31] to model oblique shocks
in uniform density medi a. Figures 1 and 2 show results obtain ed for a shock that has evolved
to a steady- state structur e. As shown by Wardle [29] when field rotation is signific ant the
trajectory in By , Bz phase space corresponds to a spiral node in the vicini ty of the upstream
fast-mode state. As seen from Figures 1 and 2, the veloc ity structure is compl icated where
magnet ic field rot ation is significan t.
11The availability of a time-dependent code opens the possibility of studying shocks in
inhomogeneous media. Star forming regions conta in density structures on a variety of scales
and, as ment ioned in Section 4, the respon ses of such structures to shocks determ ine whether
star formation induc es further stellar birth or causes it to cease. Ashmore et al [33] used the
Falle- Van Loo et al. code to study obliqu e shocks in inhomogeneous star forming regions.
Results simi lar to those that they present ed are displayed in Figure 3.
8. Conclusion
The major challenge in star formation theory will be the incorpora tion of the effects of dust in
multidimensional, time- dependent magne tohydrodynam ic simul ations. The work reported in
many of the papers cited in this brief review demonstrates the exist ence of a community that
appreci ates the role that dust plays in the phenomena invest igated in simula tions of the
dynamics of star forma tion. However , so far the assumption of non-ideal
magnetohydrodyn amics has been relaxed in only a handful of the multidimensiona l numeric al
studies, e.g. [14]. Hard but interest ing work remains.
Refer ences
[1] Trumpler , R.J., 1930, Lick. Obs. Bul l., 14, 154.
[2] Stebbins, J., H uffer, C.H. and Whitford, A.E., 1934, Publ. W ashburn O bs., 15. (V),1

thickness is roughly

Δ=VAl2

2νniVS

Δ is the lengthsca le over which dissipation occurs, and the smaller Δ is the hotter the gas

becomes. If grains were present and well- coupled to the magne tic field, the expression for Δ

would contain the sum of νni and νng , rather than νni alone. However , collisions tend to

decouple the grains from the magne tic field, an effect considered by Draine [22] and Draine,

Rober ge and Dalgarno [23] whose models of perpendicul ar shocks are reliab le for cases in

which the preshock value of nH is ≤ 106 cm-3.

8At higher densit ies a self consisten t calcul ation of the average charge on the grains and the

fraction al ioniz ation is required to obtain accurat e results for νni and for the effect that grains

have on the shock structure. Pilipp, Hartquist and Havnes [24] includ ed such a calculation in

each of their models of perpendi cular shocks. They also includ ed fluid equations for the

grains rather than adop t a simpl er approxi mation to calculate the effects of dust [22, 23]. This

led them to discover a run-away proces s operat ing in perpend icular shocks for which the

preshock value of nH is 107 cm-3 or highe r. At such densities, the ratio of n(e)/|Zg|ng drops

below unity within the precursors of sufficiently fast shocks. n(e) is the electron number

density , |Zg|e is the magni tude of the average charge carried by grains and ng is the number

density of grains. Once this ratio drops below unity , |Zg| begins to drop as there are

insuf ficien t electrons to continue charging the grains. Assume that the shock propagates in

the x-direc tion and the magnet ic field is in the y-direct ion and that Ω/νgn , the grain Hall

parame ter, is small. Then the grains separate from the other charged particles sufficien tly to

generat e an x-compon ent of the ele ctric field with a magnitud e given approxima tely by

Ex=mgνgn∣vnx−vgx∣

∣Zg∣e

Here mg is the mass of a grain. This creat es an ion drift veloc ity componen t in the z-direc tion

with a magn itude of cEx/By . As |Zg| drops, this component of the drift velocity increases.

This causes an incre ase in the rate at which a grain exper iences collisions with ions, which

leads to a further drop in |Zg|. Hence, a runaway occurs.

The recent work of Guill et, Jones and Pineau des Forêts [25, 26] represents a signif icant

developm ent in the modeling of perpendicu lar shocks in dusty star forming regions. In their

work on C-typ e shocks [25], they adopt ed a hybrid approach. The gaseous species were

described as fluids, whereas the trajectories and charges of many individua l dust particles

were followed. The treatmen t gave self-consistent results for the grain charges, gas phase ion

9and electron abundan ces and dynam ics. Though the fluid approach of Pilipp et al. [24] is

valid for a wide range of parame ter space, the Guille t et al. [25] method is required in cases

in which dust gyroradi i are comparab le to or larger than the scales on which variations of

parame ters vary in shocks.

6. Steady-S tate Models of Oblique Shock s.

Pilipp and Hartquist [27] adopt ed a fluid description of grain dynami cs in studies of steady

shocks propagat ing obliquely to the upstrea m magnet ic field in dusty star forming regions.

We will assume that a shock propagates in the x-dire ction and that the upstream magn etic

field has x and y componen ts but its z component is zero. They found that grain-neutr al

collisions lead to a rotation of the magneti c field in a C-type shock precursor around the x-

direct ion.

The following considera tions show why such rotation occurs. In the shock frame the z-

component of the electr ic field, Ez , is VSBy0/c , where By0 is the y-componen t of the upstream

magnet ic field. Thus, there is a componen t of ExB drift in the x-dire ction. In the absenc e of

collisions, the x-compon ents of the ExB drift velocities of all species are equal. However ,

grain-neutr al collisions are signific ant leading to a non-zero x-component of the Hall current.

For a steady shock, the equa tion of charge conserva tion requires that the x-component of the

total current is zero. Thus, a current parallel to the magneti c field having a x-componen t that

cance ls the Hall current component in the x direc tion must exist. Use of Ampere ’s Law sho ws

that the curren t along the magnet ic field gener ates a component of the magne tic field in the z

direct ion.

By integrat ing from an upstrea m point in the downstrea m direct ion, Pilipp and Hartquist [27]

succeeded in finding only intermedi ate-mode shock solutions. Such solutions are

inadm issible [28].

10Wardle [29] showed that integra tion in the downstrea m direc tion will not yield steady fast-

mode solut ions because the down stream state corresponds to a saddle point. He found fast-

mode solut ions by integra ting upstream from the downstream state.

Chapman and Wardle [30] have extended this work and shown that the inclusion of PAHs

leads to a drop in the gas phase electron abundance and enhanc ed rotation of the magn etic

field. PAHs are nano-part icles thought to be abundant in clouds more diffuse than star

forming regions. As mentioned earlier, in such regions desorpt ion of material from the gas

phase may result in a ll part icles gro wing to sizes close to 0.1 μm.

Integrat ion in the upstream direc tion is not appropri ate if condi tions anywhere in a shock

deviat e from equilibr ium. After shocked gas has cooled, the abundanc e of H2O, an impor tant

coolant in shocked dense core mater ial, remains far from its equil ibrium value for many times

the flow t ime through a shock. Other che mical species also have abundances that are far from

their equilibr ium values for considerab le periods. Consequen tly, the calcula tion of shock

structures by integrat ion in the upstream direc tion is inappropr iate, and the use of a time-

dependent, rather than a steady-state, approa ch is necessary to overcome the difficulties found

by Pilipp and Hartquist [27] and explain ed by Wardle [29]. Falle [31] has deve loped an

appropriat e time-depend ent approach.

7. Time-Depen dent Mode ls of Oblique Shock s in Dusty R egions.

Van Loo et al. [32] have used the techn ique deve loped by Falle [31] to model oblique shocks

in uniform density medi a. Figures 1 and 2 show results obtain ed for a shock that has evolved

to a steady- state structur e. As shown by Wardle [29] when field rotation is signific ant the

trajectory in By , Bz phase space corresponds to a spiral node in the vicini ty of the upstream

fast-mode state. As seen from Figures 1 and 2, the veloc ity structure is compl icated where

magnet ic field rot ation is significan t.

11The availability of a time-dependent code opens the possibility of studying shocks in

inhomogeneous media. Star forming regions conta in density structures on a variety of scales

and, as ment ioned in Section 4, the respon ses of such structures to shocks determ ine whether

star formation induc es further stellar birth or causes it to cease. Ashmore et al [33] used the

Falle- Van Loo et al. code to study obliqu e shocks in inhomogeneous star forming regions.

Results simi lar to those that they present ed are displayed in Figure 3.

8. Conclusion

The major challenge in star formation theory will be the incorpora tion of the effects of dust in

multidimensional, time- dependent magne tohydrodynam ic simul ations. The work reported in

many of the papers cited in this brief review demonstrates the exist ence of a community that

appreci ates the role that dust plays in the phenomena invest igated in simula tions of the

dynamics of star forma tion. However , so far the assumption of non-ideal

magnetohydrodyn amics has been relaxed in only a handful of the multidimensiona l numeric al

studies, e.g. [14]. Hard but interest ing work remains.

Refer ences

[1] Trumpler , R.J., 1930, Lick. Obs. Bul l., 14, 154.

[2] Stebbins, J., H uffer, C.H. and Whitford, A.E., 1934, Publ. W ashburn O bs., 15. (V),1