AGN Feedback w/ angular momentum

[bottom]

Research Project started from Nov. 2015 @ SHAO

16.12.09

updated physics from Gan+14
ms.pdf / updated one: 161222_newphysics.pdf [note that 3R_s should be replaced by 10R_s in eq.(3)]

16.10.09

  • Currently, the stellar rotation velocity is set to be $v_{\phi,\star}= k_{\star}*v_{\phi,kep}$, where $k_{\star}=0.5$ as a fiducial set. However, $k_{\star}$ may or may not be somewhat overestimated, in a sense that the size of the accretion disk is proportion to the stellar rotation velocity (see figures below), and subsequently is anti-proportion to the accretion rate onto the black hole.
    • Which $k_{\star}$ value we can use as a standard one?? This probably is subject to the target from lower rotation E0 galaxy to higher rotation E9 galaxy.
    • Most importantly, now we can think that the accretion rate onto the black hole can be determined mainly from two factors: $\alpha ~\& ~k_{\star}$ !!!
161003_show5_y41-y49.png
161003_ksfcomp.png
161003_ksfcomp_disksize.png
  • Also, we need to be careful for setting $v_{\phi,\star}$ in terms of $\theta$ dependency. In the current model, the stellar rotation is not depend on the $\theta$, however it probably causes some problem that at higher latitude, the stellar rotation (i.e. initial gas rotation from the star) can be super-keplerian. For instance, if $k_{\star}=0.5$, the rotation velocity will be larger than keplerian velocity in the region where $\theta<30^{\circ}$.
    • Therefore, we may need to set the $\theta$ dependency on the stellar rotation velocity.
      $v_{\phi,\star} = k_{\star}*v_{\phi,kep} * \sin{\theta}$
  • In case of model y24 ($\alpha=0.1$ & AGN FB on), the AGN activity was turned on and occasionally broke the accretion disk at earlier moment. However, something occurred in the outer region of galaxy that temperature became very high, radial and rotation velocities are also increased sharply. Those phenomena looks not physical. See the animation and the snapshot below.
Animation of the model y24
play4_y24
161010_show4_y24_327.png

16.09.15

  • the viscosity time scale is significantly shorter than the hydrodynamic time scale in larger $\alpha$ > 0.1 that it is almost impossible to proceed the run.
    • needs to approximation !!
      -> if $\tau_{visc,min} < \tau_{hydro}$, we consider the time after $\tau_{visc,min}$ as a free-fall.
    • two different order of the approximation: 1st & 2nd
      -> it seemed 1st-order approx. working fine but 2nd-order approx. have some trouble generating weirdly exaggerated $v_{\phi}$.

16.08.18

  • Results for testing viscosity routine: examine the relationship bet. the $\alpha$ and the inflowing $v_{r}$
    • Two methods: Left figure- $\nu \propto r^{1/2}$ and Right figure- $\nu \propto c_{s}^{2}/\Omega_{k}$
    • Both methods apparently show that the inflow radial velocity is proportion to the $\alpha$ parameter
160818_vravet_f01f05.png
160818_vravet_e02e06.png
Animation
no viscosity (ssa=0), where ssa$\equiv \alpha$
$\nu \propto r^{1/2}$ - Stone et al. 1999
ssa=1e-3 ssa=1e-2 ssa=2e-2 ssa=3e-2 ssa=4e-2
$\nu \propto c_{s}^{2}/\Omega_{k}$
ssa=1e-3 ssa=1e-2 ssa=2e-2 ssa=3e-2 ssa=4e-2

16.07.26

  • Derived the normalization factor for testing Stone et al. 1999 : »» alphanorm.pdf ««

16.07.25

  • The alternative shear viscosity coefficients (Su et al. 2016): leading-order Braginskii viscosity
(1)
\begin{align} \eta =& 0.406 \frac{m_{i}^{1/2} (k_{B}\,T)^{5/2}}{{Ze}^{4}\,{\rm ln\,\Lambda}} \frac{F_{i}}{1+4.2\,l_{e}/l_{T}} \nonumber \\ =& \frac{4.5\times10^{-17}\,F_{i}}{1+4.2\,l_{e}/l_{T}}\,T^{5/2} ~~~ [{\rm g\,s^{-1}\,cm^{-1}}] \end{align}

16.07.22

  • Start to use new cluster (ln01): quick benchmark
    • "ln01" is 40% faster than "bright60" and "bright61" is 20% slower than "bright60".
      Best choice: ln01 !!!
    • Note that the number of processors per node is 12, 16, 32 for "bright60", "bright61", "ln01", respectively.
160722_bench_cluster.png
160722_bench_cluster2.png

16.07.20

  • WHY the plateau appears at r < 100pc regardless of the $\alpha$???
    • Angular momentum is not important?
  • forces profile: total gravity($f_{grav}$) = black hole ($f_{bh}$) + dark matter($f_{dm}$). and $f_{cnt}$ is a centrifugal force
    • the gravity of dark matter becomes dominant as r > 10 pc (vertical dotted line)
  • Except for the case $\alpha=1$, gravity is well balanced by the centrifugal force in small radius. (i.e. rotation supported disk has formed.)
160720_forces_m01.png
160720_forces_m02.png
160720_forces_m03.png
160720_forces_m04.png
  • Like to the forces above, the rotation velocity profile (mass-weighted average: solid line) is consistent with the keplerian rotation velocity except for the case $\alpha=1$
160720_forces_m01_vphi.png
160720_forces_m02_vphi.png
160720_forces_m03_vphi.png
160720_forces_m04_vphi.png

16.07.19

  • Figures below show the velocity profiles (mid plane) for the different $\alpha$ from 1e-3 to 1.
    • Up to $\alpha=0.1$, the disk looks being supported by the angular momentum (i.e. the rotational velocity is consistent with the keplerian velocity),
      However, in the case of $\alpha=1$, the rotational velocity is very smaller than the keplerian value.
160719_freevelcmp_m01.png
160719_freevelcmp_m02.png
160719_freevelcmp_m03.png
160719_freevelcmp_m04.png

16.07.18

  • Inward radial velocity increases and the location of maximum inward (negative) velocity goes closer to the nucleus as the $\alpha$ increases. (See figure below)
  • However, at r < 100 pc, the inward velocities are not distinguishable.
160718_vrave_m01_m03.png
  • The evolution of black hole mass & mass accretion rate
160718_bhmass_m01_m03.png
160718_bhmass_ZGan.png

16.07.14

  • Every simulations with $\alpha >1$ is running extremely slowly, or looks almost suspended.
    • Possibly caused by very small viscosity time scale resulting in huge number of subcycle,
    • or, the integer "nvisc" is overflowed.
      -> No error message so far, but in order to be clear for the latter case, I modified the code regarding with the "nvisc"-problem.

16.07.13

  • Animated clips for the models
    • Label: agnRot_m01/agnRot_m02/agnRot_m03/agnRot_m04 => $\alpha$ parameter is $10^{-3}\,/10^{-2}\,/10^{-1}\,/1$
Animation
agnRot_m01 (ssa=1e-3) agnRot_m02 (ssa = 1e-2) agnRot_m03 (ssa=1e-1) agnRot_m04 (ssa=1)
  • Density & radial velocity comparison (Figures below)
    • The dynamical evolution of the models "agnRot_m01" & "agnRot_m02" look similar, but it is different for the model with higher $\alpha$ parameter
      -> cold equatorial disk disappears. more spherically accreting into the nucleus.
      -> Why?? Probably, the viscosity time scale becomes smaller than the cooling time scale ?
160713_m01_m04_d.png
160713_m01_m04_vr.png

16.07.12

  • We set the rotation of the star from simple k-decomposition with $k_{\star}=0.5$, which is a half of keplerian rotational velocity.
    • This is somewhat arbitrary. Why do we set the star's rotation as sub-keplerian?
  • Figures below: The comparison between the hydrodynamic time scale and the viscosity time scale
    • Label: agnRot_m01/agnRot_m02/agnRot_m03/agnRot_m04 => $\alpha$ parameter is $10^{-3}\,/10^{-2}\,/10^{-1}\,/1$
    • As expected, if the alpha parameter increases, the viscosity time scale becomes smaller.
    • the case of $\alpha=1$, the overall evolution is quite different with others
    • Label: angRot_l01 is same with agnRot_m01 but different method in calculating the viscosity time scale.
      • agnRot_l01 used diffusive time scale as the viscosity time scale, but other models calculated the times scale directly from the change rate.
        I will use the direct calculation for rest simulations, although it looked similar in order of magnitude between them.
160712_dtvisc_agnRot_m01.png
160712_dtvisc_agnRot_m02.png
160712_dtvisc_agnRot_m03.png
160712_dtvisc_agnRot_m04.png
160712_dtvisc_agnRot_l01.png

Email from Prof. Yuan
Luca and Zhaoming have finished the setting of the angular momentum in the code. Now let me briefly summarize what we have discussed on the mechanism of angular momentum transfer, which mainly come from Jerry's advices. We have discussed three mechanisms: 1) alpha viscosity whose physics may be MRI in accretion disk; 2) viscosity due to the gravitational instability; and 3) a new mechanism proposed by Hopkins & Quataert (2011, MNRAS, 415, 1027), as firstly suggested by Jerry.
We decided to proceed by testing the first one. DooSoo has finished this test. He found that this mechanism is not so efficient in the sense that the resultant mass accretion rate is very low. This is in some sense what we expect.
For the second mechanism, Jerry once provided some nice equations (see the message appended below). Now DooSoo is working on it. While I agree with Jerry about the physics, I have two concerns. One is that I feel the equations provided by Jerry is somewhat phenomenological and arbitrary. As a comparison, Charles Gammie once did detailed numerical study to the gravitational instability, focusing on its role of angular momentum transfer (Gammie 2001, ApJ, 553, 174). Based on the simulation, he provided a formula of 'alpha' to calculate the angular momentum transfer. This looks to me more physical and precise. It is also convenient to use. Should we use it if we think gravitational instability is the dominant mechanism?
The next concern is related to the third mechanism of angular momentum transfer proposed by Hopkins & Quataert (2011). Gravitational instability may not be the dominant mechanism of transfer angular momentum, according to this work. As you can see from this paper, they propose that the strongest torque arises when non-axisymmetric perturbations to the stellar gravitational potential produce orbit crossings and shocks in the gas. They provide the analytical formula for the torque and compare the results (on accretion rate and so on) based on this torque with their numerical simulations and find good agreement. Note that they also consider the 'local viscosity' such as those arisen by the gravitational instability and conclude that their new mechanism is dominant. So my question is that should we adopt this mechanism in our project?

16.07.09

  • Full description of viscosity stress tensor in spherical coordinates: »»> viscTensor.pdf ««<

16.07.08

  • Major reason of code crash:
    • overestimated $t_{visc}$ -> the rotational velocity increases hugely even in small iteration, then end up with infinity.
    • I calculated the viscous time scale in two different way: 1. diffusive time scale 2. direct calculation from v / change rate
    • Since our work has complicated physics possibly producing non-smooth features in density, velocity gradient (shears), so
      the second method should be more appropriate.
  • TODO:
    • derive stress-tensors in every direction.
    • currently we only consider Toroidal Tensors ($T_{r\phi}, T_{\theta\phi}$), since they are dominant in the disk-like structure.
    • However, if the AGN Feedback is introduced, the shears in radial direction should not be ignorable.
  • Hoiland Criteria - The Holland criterion for static rotating fluid states that the fluid is stable against local, axisymmetric,
    adiabatic perturba- tions if and only if the following two conditions are satisfied (see Tassoul 1978 for details; Igumenshchev 1995)
(2)
\begin{align} \frac{1}{r^{3}}\frac{\partial l^{2}}{\partial r} - \left( \frac{\partial T}{\partial P} \right)_{s}\, \nabla P \cdot \nabla S > 0 \\ -\frac{1}{\rho}\frac{\partial P}{\partial z} \left( \frac{\partial l^{2}}{\partial r} \frac{\partial S}{\partial z} - \frac{\partial l^{2}}{\partial z} \frac{\partial S}{\partial r} \right) > 0, \end{align}

where S is the specific entropy.

16.07.06

  • Uncertainty Principal !!!: whenever restarting, the result is slightly different from the data started from the initial condition.
    • This may be a serious problem. We cannot believe the result from the restarting scratch file.
    • I found some enhanced inflow right after restarting. But it looked like caused by intrinsically.
      I turned off any source steps, but still this happened.
    • Something is not good. It looked the error is larger than truncation error. (sometimes the error > 1%)
      • We need to be careful if we restart it.
160706_unctest.png

16.07.04

Email from Prof. Ostriker to Prof. Yuan
I have just been chatting with Yanfei Jiang who has recently come back from a good visit with you and I wanted to get back to our discussion.
We agree on the problem to be addressed and only are leaving as a question how we should model the viscosity/angular momentum transport. There are two approaches that have been proposed, one is “alpha-based” and is similar to what Gammie (2001) proposed, and it basically keeps the disc near marginal local (Toomre) stability. The other is Hopkins & Quataert (2001) and is similar to the old Peebles & Ostriker bar mode criterion. I think that ** in their application the two approaches would only differ in detail **, and perhaps it is best to be agnostic and try both approaches. They are both to be implemented in a rather easy and straightforward manner.

reply from Prof. Yuan to Prof. Ostriker
First, it is impossible for our 2D simulation to include either one of them from first-principle. So we have to be satisfied with some phenomenological description, i.e., alpha description.
The Gammie (2001) mechanism can be described and implemented by a ** phenomenological alpha description . Strictly speaking, ** this is true only if the disk does not fragment **. But we may still adopt it in our work for simplicity(? ). We should include a term in both the momentum and energy equations as in the standard phenomenological accretion disk models. To be more specific, there are two stresses in the Gammie model, one being the hydro stress and another the gravitational stress. Physically, the energy dissipation term includes both the cascade of turbulence (for the hydro stress) and dissipation of shock (for the gravitational stress). If instead we are simulating the disk in the first-principle way, all these are automatically included so there will be no need to explicitly including the alpha terms in the momentum and energy equations.
I have checked the above statement with Charles.
The Hopkins & Quataert (2011) mechanism is more complicated. The intrinsic feature of the Hopkins model is the non-axisymmetric distribution to the stellar gravitational potential which causes gravitational torque. This seems to physically somewhat different from the Gammie model. In section 5.1 of their paper, they compared their model result with the local alpha model (which may include the Gammie model). They concluded that their model is better in terms of producing a correct inflow rate (obtained from their detailed numerical simulations) and so on.
Since our simulation is 2D, we have to adopt a phenomenological description. The following work gives us an example. They use the Hopkins model:
http://adsabs.harvard.edu/abs/2015MNRAS.454.1038R
Specifically, they also use a phenomenological alpha description. So maybe same with this paper, we can also use an alpha description for the angular momentum transfer? In this case, ** the implementation of the alpha term in the momentum equation will be same with the above Gammie alpha model.
This is also what you suggested if I understand you correctly. Of course, the value of alpha in this case can be much larger than one, which is different from the Gammie model.
However, there may be one important difference. I discussed with my group members, we feel it may be different for the energy equation. The ** Hopkins & Quataert mechanism just transfer the rotation energy of the gas from the disk to the stars, so there may be no energy dissipation term in our energy equation. **

  • Possible reason of Code Crash:
    • Internal energy in Ghost shells is not updated properly.
    • "bvstat" is not a function -> updating energy by "bvale" function !!
  • Benchmark for the performance
    • Grid dimension: 120x30 -> in this case, 8 processors seem to be most efficient for carrying out the simulation with. (See below)
    • "Bright60" is faster than "Bright61" in my runs !!!
    • But note that the number of processors per node is 12 in Bright60 and 16 in Bright 61
160704_bench_cluster.png

16.07.03

  • upper line: 4 right most values in left block (2 right ones are ghost shell)
    lower line: 4 left most values in right block (2 left ones are ghost shell)
    • Looks like updating not good
r
   0.00957829    0.0105558    0.0116310    0.0128138
   0.00957829    0.0105558    0.0116310    0.0128138
th
     0.863937     0.863937     0.863937     0.863937
     0.863937     0.863937     0.863937     0.863937
d
  4.40198e-08  3.81769e-08  3.33756e-08  2.38778e-08
  3.40746e-08  3.81769e-08  3.33756e-08  2.94281e-08
v3
      97.5146      92.5428      87.1544      81.4071
      97.5146      92.5428      87.1544      81.4071
e
    0.0151679    0.0123409   0.00708379  0.000139322
  0.000149188    0.0123409    0.0100603   0.00821648

16.07.02

  • mpich2 was failed for installation in the desktop because gfortran is not compatible with the package. (maybe f77 or ifort is required.)
    • cluster server forbid to use Normal Queue (mpi run) for a single process. —> Only use Serial Queue for a single core.
      However, the zeus_mp code is optimized in MPI-configuration. It may take some wasteful time to modify the code to fit Serial run.

16.07.01

Group meeting

  • all directions of tensor may need to be taken into account, although $\phi$ component is still dominant one.

16.06.30

  • TODO
    • resolve what is happening in the ghost shell
      why it worked in most cases and it didn't work in the particular case (cooling & viscosity)?
    • resolve the "restarting problem"
      • If I restart from the scratch file not from initial, the code is working but the result is slightly different.
        • Probably cleaned up the truncation errors or some mis-reading the parameters (Have to check for future running)
    • Back to the Hopkins paper and find proper value of alpha for showing the reasonable inflow rate.
      • will run several runs with different alpha values (including cooling & viscosity but no AGN FB)

16.06.28

160601_agnRot_e01_dvr.png
160629_nanplace_2.png
  • Code crash problem
    • Thermal Instability? -> tested w/ an order lower density but still have same problem
      • Not likely
    • Divergence of the velocity field (left panel of the figure above)
      • Not likely: See right panel which shows where the "NAN" values occurs at the first moment of code crash
        Looks like it happens uniformly not just at the region of the large velocity gradient. (NAN region -> cyan diamond in right panel)
    • Checked the place where it crashed in the code
      • not in source code but right after the transport code
        I should not modify the transport code because it is core of the ZEUS.
    • some glitches for dealing w/ viscosity time scale => should be same value for entire domain
      otherwise, problem will take place while communicating for each blocks
    • it has no problem if the simulation use a single core (no multi-processors)
      • should figure out what is going on the ghost shell !!

16.05.05

Group meeting

  • Test with simple accreting black hole problem (dynamical range decrease to kpc)
    only BH potential (turn off dark mater potential) & check $v_{r,inflow} \propto \alpha$

16.04.29

Group meeting

  • Check the viscosity time scale if it is, at least, comparable to the dynamical time scale.
    • be careful of normalization ($\propto \sqrt{G\,M}$)
    • suggested to calculate the viscosity time scale by $v_{\phi} / v_{rp}$, where $v_{rp}$ is angular momentum transport rate.
  • viscosity formula should be modified.
    • Previous formula: $\nu = C\,r^{1/2}$, where $\nu$ is the kinematic viscosity.
(3)
\begin{align} \nu=\alpha\frac{c_{s}^2}{\Omega_{k}} \end{align}

16.04.26

  • adopt the $\alpha$-disk formula in Stone et al. 1999 for describing the angular momentum transport by the non-axisymmetric gravitational torque (no MRI). (See Rosas-Guevara et al. 2015)
    • $\nu = C r^{1/2}$, where $\nu$ is kinematic viscosity (see Stone et al. 1999)
    • standard value of $C$ in the literature is $10^{-3}$
    • Now we play with $C=10^{-3},10^{-1},10,10^{3},10^{5}$ to find appropriate value to be consistent with the analytic expectation by Hopkins & Quataert 2010.
  • Note that the accreting time scale by the viscous stress should be comparable with the star formation time scale (i.e. $\tau_{visc} \sim \tau_{SF}$)
    • dumped out the $\tau_{SF}$ in the hdf data set (modified hdfall.F routine, which is called from dataio.F)
      —> also need to modify auto_h4.F in pp folder: increase nfunc (nfunc = nfunc + 1)
    • $\tau_{visc} \sim \tau_{accr} = \frac{r}{v_{r}}$, where $v_{r}$ is radial velocity of hot medium (not including stellar objects.)
      —> identify the hot medium by the temperature $T_{hot} \sim 10^{6}\,K$

16.04.07

Email from Prof. Yuan to Prof. Ostriker
Luca and Zhaoming have finished the setting of the angular momentum in the code. Now let me briefly summarize what we have discussed on the mechanism of angular momentum transfer, which mainly come from Jerry's advices. We have discussed three mechanisms: 1) alpha viscosity whose physics may be MRI in accretion disk; 2) viscosity due to the gravitational instability; and 3) a new mechanism proposed by Hopkins & Quataert (2011, MNRAS, 415, 1027), as firstly suggested by Jerry.
We decided to proceed by testing the first one. DooSoo has finished this test. He found that this mechanism is not so efficient in the sense that the resultant mass accretion rate is very low. This is in some sense what we expect.
For the second mechanism, Jerry once provided some nice equations (see the message appended below). Now DooSoo is working on it. While I agree with Jerry about the physics, I have two concerns. One is that I feel the equations provided by Jerry is somewhat phenomenological and arbitrary. As a comparison, Charles Gammie once did detailed numerical study to the gravitational instability, focusing on its role of angular momentum transfer (Gammie 2001, ApJ, 553, 174). Based on the simulation, he provided a formula of 'alpha' to calculate the angular momentum transfer. This looks to me more physical and precise. It is also convenient to use. Should we use it if we think gravitational instability is the dominant mechanism?
The next concern is related to the third mechanism of angular momentum transfer proposed by Hopkins & Quataert (2011). Gravitational instability may not be the dominant mechanism of transfer angular momentum, according to this work. As you can see from this paper, they propose that the strongest torque arises when non-axisymmetric perturbations to the stellar gravitational potential produce orbit crossings and shocks in the gas. They provide the analytical formula for the torque and compare the results (on accretion rate and so on) based on this torque with their numerical simulations and find good agreement. Note that they also consider the 'local viscosity' such as those arisen by the gravitational instability and conclude that their new mechanism is dominant. So my question is that should we adopt this mechanism in our project?

Reply from Prof. Ostriker to Prof. Yuan
There may be very little difference between options (2) and (3), since both transfer angular momentum at a significant rate (I believe) only when Toomre stability is violated and then the maximum rate of angular momentum loss (transfer) is dj/dt,max = Omega*j.

Reply from Prof. Yuan to Prof. Ostriker
Option (2), i.e., the stress due to the gravitational instabiliity, can be described by a local alpha desciption as suggested by Gammie (2001). Note that such a local alpha treatment is only applicable when a large-scale external force is absent. I am not sure whether this is applicable to our case.
In section 5.1 of Hopkins & Quataert (2011), they compare their model (i.e., option 3) with the local alpha model which may include the gravitational instability model of Gammie (2001). By comparing with their numerical simulation results, they conclude that their model (option 3) is better than the local alpha model (option 2).


Email from Prof. Yuan to Prof. Gammie
I am reading your famous paper on gravitational instability (Gammie 2001, ApJ) together with two members of my group. We have the following questions to ask for your advice. The stress consists of two parts, namely the hydrodynamical part and the gravitational part. My first question is that whether they can produce local energy dissipation? My second question is how to write the corresponding terms in the energy equation?

Reply from Prof. Gammie to Prof. Yuan
Yes, the stress can produce dissipation that is local in the sense that energy extracted from the shear is thermalized within a few scale heights.
This claim has been a little bit controversial: Balbus & Papaloizou 1999 argued that gravity produces nonlocal dissipation. But the claim of nonlocal dissipation is not born out by simulations (see Ken Rice's recent review, \S 2.2) as long as H/R « 1.
If you are asking whether the stress and dissipation are local in the sense that for each (x,y,z) the stress = alpha x pressure, and dissipation = stress x rate-of-strain, then no, the dissipation is not local in that sense. But averaged over a column through the disk and averaged over time, dissipation is directly related to the stress and the integrated pressure.
Not sure what you mean by corresponding terms in the energy equation. Do you mean you are writing a phenomenological model for disk evolution? In that case the gravitational/hydro stress can be treated like an alpha model. If you are looking for a first-principles description then the energy equation is given in the paper and contains the usual hydrodynamic and gravitational terms. I do not think there is anything in between the alpha prescription (time and column averaged) and the first-principles description.

16.03.14

  • completed to develop the subroutine for the angular momentum loss by gravitational instability (Prof. Ostriker)
    —> »»> grav_tech.pdf ««<

16.03.01

  • completed the run for the models at which the rotation is included w/ angular momentum transport by viscous stress (viscosity parameter=1.d-3 or 1.d-2).
    —> combined movie clip

16.02.26

  • completed the run both non-rotating (Gan et al. 2014) & rotating w/o angular momentum transport
  • implemented the subroutine of angular momentum transport by shear stress mimicking magneto-rotational instability (Stone et al. 1999)
    —> alpha_old.F
    • run two simulations with ssa=1.d-3 (Stone et al.1999) and 1.d-2 (more viscous)
  • TODO: implement the subroutines of angular momentum transport by
    • gravitational torque (Prof. Ostriker's note (gravInst.pdf) or Gammie 2001)
    • asymmetric potential (bar-within-bar; Hopkins & Quataert 2010, 2011)

16.01.28

  • re-derived the gravitational instability analysis (suggested by Prof. Ostriker) and found the formula of
    • the variation of angular momentum
    • thermal heating
      in the sense of Eulerian so that we can apply it into the ZEUS code.
      —> »»> gravInst.pdf ««<
  1. How we can estimate the surface density? (integrate along $\theta$)
    1. then, we need to update the angular momentum & thermal energy heating only within the integrated area or entire domain?
  2. velocity profile (flat rotation or hybrid profile (near black hole: Keplerian?)
  3. epicycle frequency -> assumed the constant angular momentum (is it okay?)

16.01.25

  • Run a test simulation for rotating galaxy (simplified k-decomposition)
    • $v_{\phi} = k\,\sigma$
    • thermal heating by the relative velocity between mass loss stars (mainly AGB stars) and ISM: multiply a factor of $1-k^{2}/3$
      -> increased k (faster rotating) implies decreased portion of thermal heating, (i.e., more contribution to kinetic energy)
    • $k=0.5$ is constant: so this test run is not self-consistent in the evolution of stellar distribution

15.12.30

  • initial condition (noc.F)
  • source term (src.usr & srcstep.F)
  • units (rad.F)
    • Length = 10 kpc ($3.08\times10^{21}$ cm), Time = 1 Gyr ($3.15\times10^{16}$ s), Mass = $2.5\times10^7 M_{\odot}$ ($4.97\times10^{40}$ g)
  • parameters including boundary conditions (zmp_inp)

15.12.17

Regulate the growth of SMBH and the evolution of the galaxy
  1. accretion (small scale; stellar evolutionary process and dynamical relaxation; in smaller EGs) and merger (large scale; larger EGs)
  2. AGN Feedback
  3. evolution of disk instabilities (gas inflows into SHBH)
  4. minor mergers are a significant component of the late-time stellar mass growth of the most massive galaxies.
  • Since BH–BH mergers will be accompanied by the gravitational slingshot effect (Peres 1962; Bekenstein 1973; Fitchett & Detweiler 1984), late time mergers may eject a significant amount of mass in BHs from merged galaxies.

UNDERSTANDING BLACK HOLE MASS ASSEMBLY VIA ACCRETION AND MERGERS AT LATE TIMES IN COSMOLOGICAL SIMULATIONS (Kulier et al. 2015)

  • gas accretion remains the dominant source of mass accumulation in almost all SMBHs, rather than mass supply from merger event

Black Hole Masses and Eddington Ratios at 0.3 < z < 4 (Kollmeier et al. 2006)

  • Supermassive BHs gain most of their mass while radiating close to the Eddington limit, and they suggest that the fueling rates in luminous AGNs are ultimately determined by BH self-regulation of the accretion flow rather than galactic-scale dynamical disturbances.

Feedback from active galactic nuclei: energy- versus momentum-driving (Costa et al. 2014)

  • Momentum-driven wind: If the reverse shock cools efficiently, shocked inner wind gas traverses a radiative region with a size of the order of the cooling length until its temperature returns to its pre-shock value at a radius≈Rr +lcool. This sequence of an initially adiabatic shock and a cooling region constitutes an isothermal shock. Since cooling at a radius≈Rr +lcool. This sequence of an initially adiabatic shock and a cooling region constitutes an isothermal shock.
    The inner wind can then be imagined to collide with the ISM directly, transferring its momentum fully in the interaction. In this limit, the outflow is said to be momentum-driven since the driving force is equal to the momentum flux of the innerwind.
  • Energy-driven wind: If the reverse shock is instead unable to radiate away its thermal energy, the shell is driven by the adiabatic expansion of the hot shocked wind bubble (see Fig. 2). In the limit where the full energy of the inner wind is conserved, the resulting outflow pattern is termed energy-driven.
mom_ener_wind.png

15.12.15

  • implementing rotation of the galaxy (v_phi): "k-decomposition"

(galaxy_rotation.pdf)

As proposed by Luca, the simplest way for me to include rotation might be the "k-decomposition", in which one needs the "decomposition" factor "1-(k^2)/3". I'v already started an experimental run, in which I made the following modifications:
(1) multiply the stellar-thermalization heating term by a factor of 1-(k^2)/3
(2) set the rotating velocity v_phi of the mass loss as v_phi = k*sigma (note that the thermalization due to the relative velocity of the source and the fluid is already considered in the code

15.12.14

15.12.09

email from Dr. Gan
Regarding the source terms, you could have a look at the file “src.usr” which is included in the source code “srcstep.F”. While the initial condition is in the file “noc.F”, and boundary conditions are specified in the input file “zmp_inp”.

15.12.08

email from Dr. Gan
What we are interested on in this project are the feeding and feedback processes in elliptical galaxies. So far, we studied intensively the cases of feeding gas with only low angular momentum, so no disk forms in our computational domain. But in reality, the ISM could have significant angular momentum even in elliptical galaxies (see the note “galaxy_rotation.pdf"), that is to say, we need ANGULAR MOMENTUM TRANSFER before the ISM could be accreted. At the meanwhile, also because of the barrier of large angular momentum, the ISM will concentrate onto the equatorial plane, then the density there will increase, and so does the infalling time, but in contrary radiative cooling time decreases, and that is how RADIATIVE COOLING comes into the problem. Then the good news is, the surface density of the newly formed disk will increase when the feeding ISM cools down, as a result, the disk could become gravitationally unstable — and GRAVITATIONAL INSTABILITY could help to transfer angular momentum (see the note “grav.instability.pdf”), this is good for the feeding process! However, there is also a bad news — because of the run-away characteristic of radiative cooling, STAR FORMATION will also come into the problem when the density increases and temperature decreases significantly. Star formation has the ability to consume most (if not all) of the feeding gas before it could be accreted (i.e., turns it into stars), which is not good for the feeding process. After modelling the processes above, we could get the accretion rate (as a function of time), and then we could put in our AGN feedback models, and to see how it works in such cases.

At the current stage, we probably need to do:

  1. modify the galaxy profile, to include rotation (see also the note “galaxy_rotation.pdf" );
  2. put in the physics of angular momentum transfer, e.g., viscosity, effects of gravitational instability (see also the note “grav.instability.pdf”);

15.12.05

  • Next step1) finding galactic profile considering considerable rotating elliptical galaxy
    • what is the general rotation speed of elliptical galaxies? and this speed is larger than velocity dispersion?
      find observational papers to support the idea of angular momentum
  • Next step2) developing angular momentum transfer like viscosity, gravitational instability …
  • caution: rotation leads more density enhancement in the galactic disk resulting in significant suffer of Thermal instability

15.11.14

Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks (Gammie 2001)

What is the definition of Gravito-turbulence??

  • If Toomre Q is high, the heating by the gravitoturbulence is week.

15.11.13

Black hole spin and the radio loud/quiet dichotomy of active galactic nuclei (Tchekhovskoy et al. 2010)

Why is the black hole spin, $\Omega_{H}$, in Elliptical Galaxy faster than that in Spiral Galaxy?

  • Galactic formation history? E-Galaxy likely formed by merger event, but why it increased the spin of the black hole?
  • Issue is that according to Blanford-Znajek theory, the radio Jet power is proportion to the spin, but its power is
    stronger in the E-Galaxy.

15.11.01.2015