crushing of interstellar gas clouds part i - thermal conduction and radiative losses -

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Crushing of interstellar gas clouds Part I - Thermal Conduction and Radiative Losses - Equations: Heat Flux: Initial conditions Cloud Mass Fraction: choose phi = 0.3 implies that no thermal precursor develops during the shock propagation, which is consistent with the fact that no precursor is observed in young and middle aged SNRs. *Zel’dovich % Raizer 1966 *Cowie & Mckee 1977

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Heat Flux:. Equations:. *Cowie & Mckee 1977. Cloud Mass Fraction:. choose phi = 0.3 implies that no thermal precursor develops during the shock propagation, which is consistent with the fact that no precursor is observed in young and middle aged SNRs. Crushing of interstellar gas clouds - PowerPoint PPT Presentation

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Page 1: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Crushing of interstellar gas cloudsPart I - Thermal Conduction and Radiative Losses -

Equations: Heat Flux:

Initial conditions

Cloud Mass Fraction: choose phi = 0.3 implies that no thermal precursor develops during the shock propagation, which is consistent with the fact that no precursor is observed in young and middle aged SNRs.

*Zel’dovich % Raizer 1966

*Cowie & Mckee 1977

Page 2: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

We may define several time scales to estimate the relative importance of different physics processes:

Cloud crushing time:

Instability growth time:

Thermal conduction time:

Radiative cooling time:

The left graph shows the relation between different time scales on a density ratio vs Mach# plot. The situations with M=30 and M=50, which will be investigated are marked.

*Mckee & Cowie 1975, KMC94,

*L is the characteristic length of T variation.

*Raymond & Smith 1977

Page 3: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Case M = 50 Mass Density (log scale)Left Panel (LP): no TC, RC.Right Panel (RP): with TC, RC.

In all stages, the thermal conduction limits the development of the instabilities.

At the cloud destruction stage, the cloud material with TC and TC is not fractioned in small cloudlets as in the left panel.

The shock transmitted into the cloud is faster and the reflected bow shock is slower than no TC case. This is due to the progressive heating of the cloud material, which makes the material behind the transmitted shock at higher T and lower rho (see P5, Panel2, B), the material behind the reflected shock at lower T (b/c the thermal energy diffuses into the ambient cloud).

Page 4: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Case M = 50 Temperature (MK)Left Panel: no TC, RC.Right Panel: with TC, RC.

Page 5: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -
Page 6: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Case M = 30 Mass Density (log scale)Left Panel (LP): no TC, RC.Right Panel (RP): with TC, RC.

During the first two stages, the thermal conduction limits the development of the instabilities.

Moreover, the strong cooling in the post-shock region results in the rapid accumulation of the cooled material in a thin dense shell. On the other hand a diluted outer part of the cloud starts to develop a hot corona with particle density 0.4 and temperature 8.0e+05. The evolution of this corona is dominated by TC. After the second stage (third panel), the cloud material evolves into cold, dense filaments under cooling whereas the corona evaporates under TC.

Page 7: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Case M = 30 Temperature (MK)Left Panel (LP): no TC, RC.Right Panel (RP): with TC, RC.

Page 8: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Quantitative study

Define cloud mass and cloud volume as:

Mixing fraction:

Average particle density:

Average mass-weighted temperature:

Average mass-weighted velocity in the direction of shock propagation:

The evolution of these averaged quantities are plotted.

Page 9: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Evolution stages:

0.0 ~ 1.0 t_cc: compressing stage1.0 ~ 1.9 t_cc: re-expansion stage 1.9 ~ 2.2 t_cc destruction stage

The mass loss is almost constant for HTR50, b/c the mechanism is now different:HTR50: cloud evaporationHY: instability ablation.

The cloud re-expands slightly earlier than HY b/c of the efficient heat up due to TC.

In the last stage, Vcl, ncl are almost almost constants, Tcl slightly increases due to the TC.

The cloud is accelerated more efficiently than HY b/c of its larger volume.

Page 10: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

The mass loss is almost constant for HTR30, b/c its TC driven. The mass exchange occurs at the hot corona.

At 0.5 t_cc, the transmitted shock becomes strongly radiative, there is no re-expansion phase in HTR30 case.

However, the temperature of the cloud decreases due to the strong radiative cooling.

Because Vcl in this case is smaller than that of other cases, the acceleration is less efficient.

Page 11: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Brief Summary of Part I

We have investigated the effect of thermal conduction and radiative cooling on cloud evolution and on the mass and energy exchange between the cloud and the surrounding medium. We have selected and explored two different physical regimes, chosen so that one or the other of the processes is dominant. In the case dominated by the radiative losses , we have found that the shocked cloud fragments into cold, dense, and compact filaments surrounded by a hot corona, which is ablated by thermal conduction. On the other hand, in the case dominated by thermal conduction, the shocked cloud evaporates in a few dynamical timescales. In both cases, we have found that thermal conduction is very effective in suppressing the hydrodynamic instabilities that would other wise develop at the cloud boundaries, preserving the cloud from complete destruction.

Page 12: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Equations:

Heat Flux:

Initial conditions

These conditions are the same as the X10 M50 runs in part I.

choose phi = 0.3 implies that no thermal precursor develops during the shock propagation, which is consistent with the fact that no precursor is observed in young and middle aged SNRs.

Crushing of interstellar gas clouds Part II - The MHD Case -

*Spitzer 1961

*Cowie % Mckee 1977

Page 13: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

We adopt a 2.5D Cartesian coordinate system, implying that the simulated clouds are cylinders extending infinitely along z axis perpendicular to the xy plane. The primary shock propagates along the y axis. We consider three B field configurations: (1) parallel to the planar shock and perpendicular to the cylindrical cloud (Bx). (2) perpendicular to both the shock front and the cloud (By). (3) parallel to both the shock and the cloud.

For post shock field strength, it has a (gamma+1)/(gamma-1) increase. We consider field strength of 2.63, 1.31, 0.26, 0 micro-G in the unperturbed medium. These values implies beta = 1, 4, 100, infinite. The conditions for different runs are summarized in the following table:

Page 14: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Beta4 runs.

External B field (Bx, By)Generally the field has two effects: (1) suppressing the heat flux and therefore the heating, (2) suppressing the HI due to the tension of the field lines, which maintain a more laminar flow around the cloud surface. However, the later effect is much weaker than that of (1). For KH, the suppression is significant when:

For RT, the suppression is significant when:

These are very strong fields and are not obvious in the simulation (top panel, NNBx compared to NN in P6).

On the other hand, HI can be efficiently suppressed by TC (all panels, compare NN with TR).

Internal B field (Bz)Internal B fields strongly suppress TC, providing an efficient thermal insulation of the cloud material. The timescale for the conduction along field lines is:

In this case, HI will develop at the cloud boundary. Also, the internal B field are expected to resist compression and thus reducing the RC, which makes the runs similar to the simulation discussed in Fragile, et al 2005.

*Mac Low, et al 1994, Jones, et al 1996

Page 15: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Beta4 runs.

Bx case: The field gradually envelop the cloud, reducing heat conduction through the cloud surface, thermal exchanges between the cloud and the surrounding medium are channeled through small regions located to the side of the cloud. Cloud expansion and evaporation are strongly limited by this confining effect. Consequently the thermal insulation induces radiative cooling and condensation of the plasma into the cloud during the phase of cloud compression. At the end of this phase the cloud material has T = 10e+05, n = 10. The field length scale can be derived (see P2):

The RC dominates over TC with dimensions larger than l. So comparing to TR on P3 , including Bx will introduce stronger HI.

By case:In this case, the initial field direction is mostly maintained in the cloud core, allowing efficient thermal exchange between the core and the upwind medium. Thus the core is gradually heated and evaporated (P14, TRBy).

Page 16: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

By case continued:

On the other hand, the cloud is thermally insulated laterally where the B field suppresses TC and induces the HI.

Quantitative Study:

We again perform quantitative studies as part I. Here, we define the following averaged quantities:

We study the effect of the thermal conduction and initial field strength on the mass mixing and energy exchange of the cloud.

Page 17: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Beta4 runs.

Mass Loss Rate: the mass loss rate in the TN models is less efficient than in the NN models. This is b/c in the TN runs, the TC can greatly suppress HI and the mass loss in TN are mainly come from the evaporation, but not HI, as discussed in part I. But notice that with B field present, the effect of TC is reduced (NN black has the smallest mass loss rate). The Bz model has the greatest reduction, making the TNBz almost the same as NNBz. B/c the internal field completely suppresses TC.

In the TR models (dashed lines), the onset of HI increases the mass loss rate of the cloud with respect to the unmagnetized case due to the fragmentation of the cloud into dense and cold cloudlets. Still, the highest mass loss efficiency is in Bz, , which is similar to NR models, as expected. TRBx and TRBy cases are intermediate between NR and TR (the field only partly reduces TC) .

Energy: The greatest value of internal energy is reached in By case, b/c this configuration allows efficient thermal exchange (heating up) as discussed on P15. This also makes By cloud has the largest cross sectional area and induces the largest kinetic energy gain. Again, Bz has the smallest energy gain b/c of the thermal insulation (similar to NR runs). Bx has the intermediate value.

Quantitative Study: Mass Loss Rate and Energy Exchange

Page 18: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Quantitative Study: Thermal Conduction Beta4 runs.

Compression and Temperature: The top and middle panels show the cloud compression (cross sectional area in the xy plane) and temperature evolution. In NN models, either with or without the B field, the evolution looks pretty the same. The cloud is initially compressed (t < 1.0) due to the ambient shock pressure, and T rapidly increases. Then, the cloud begins to re-expand leading to a decrease in T and increase in A, In the last phase ( t > 2.0) the cloud is compressed again by the Mach stem formed during the reflection of the primary shock at the symmetric axis. Comparing solid lines and dash dot lines, we find the TC is most efficient in the TN - NN case. This situation is studied in part I. In the external field case, the B field partly suppresses the TC. The By case has a larger TC effect than that in the Bx case, b/c it allows the most heat exchange between cloud and ambient medium. Bz has the smallest TC effect (almost the same as the NN case). In all, the external field partly suppresses the TC effect, making the curve located in the yellow region (between TN and NR).

Field Strength: In the case of external fields, B is mainly intensified due to the stretching of field lines caused by sheared motion. Bx case has the greatest increase, the field is mainly intensified at the cloud nose, where the background flow continues to stretch the field lines. In the By case, the increase occurs mainly at the side of the cloud.In the Bz case, the field increase is due to the squeezing of the field lines, therefore the B curve follows the A curve, since the field is locked within the cloud material. The greatest field occurs at t = 1.0, the end of the compression phase.

Page 19: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

TC also has an indirect influence on the field increase. TNBx and TNBz case show roughly the same B curve comparing to corresponding NN cases. But B field in TNBy is much smaller than that in NNBx. B/c in this case the cloud is heated up efficiently thus leads to a larger A (P18 top panel), therefore reduces the field intensity as the field is locked within the cloud material.

Quantitative Study: Initial Field Strength

The left plot shows the evolution of average mass and internal energy with different initial field strength (remember beta is the ratio between thermal energy and field energy. The greater the beta, the smaller the field) in TR models.

For Bx, the larger the beta (smaller the field), the more efficient the mass mixing. In the Bx case, the field greatly suppresses the TC, making HI the dominant process of mass mixing. On the other hand, the field can directly suppress the HI, b/c of the field tension on the surface. But recall that this suppression is very hard to achieve (needs strong field). The larger the beta (the weaker the field), the smaller this suppression is, the more efficient the mass loss (in the TR model studied here, the RC dominates b/c of the TC suppression), the less efficient the energy gain (RC dominates).

For By, the thermal exchange is efficient as discussed before. Therefore TC dominates in the TR model, the HI is greatly suppressed, the mass mixing is mainly driven by the evaporation. Thus the larger the beta (weaker the field), the smaller the TC suppression, the less efficient the mass loss, the more efficient the energy gain.

We can see from this argument the reason why the order of curves in Bx and By configuration is flipped.

Page 20: Crushing of interstellar gas clouds Part I  - Thermal Conduction and Radiative Losses -

Brief Summary on Part II

(1)B field can suppress TC. Suppression effect follows: Bz >> Bx > By

(2)B field can directly suppress HI, but needs a very strong field strength to realize. Generally the TC still acts as the major effect on suppressing HI.

(3)With different field orientation, thermal exchange occurs at different places. Bx: side of the cloud, core is dominated by cooling. By: core has efficient thermal exchange. Bz: TC completely suppressed.

(4)With TC present, B field suppresses the TC and increases the mass loss rate. The mass loss rate curve is located between TN (HI suppressed) and NR(HI not suppressed). With TC absent, B field directly suppresses HI and decreases mass loss rate (weak effect).

(5)TC dominates the energy exchange between cloud and surrounding medium. The exchange efficiency: By > Bx > Bz. For By, the weaker the field, the more efficient the energy exchange. For Bx, the stronger the field, the more efficient the energy exchange.