1. Theoretical Estimate of Intensity of Hydrogen line emission from accreting gas giants
AOYAMA, Y.,1
M. IKOMA1,
and T. Tanigawa2
1The University of Tokyo
2National Institute of Technology, Ichinoseki College
Today let me talk about Hydrogen line emission from accreting gas giants.)
[ And thank you for introducing me]
They are collaborator (Dr.) ~san

2. 1-1. Accreting Gas Giants Observation
Observational Points and Theoretical lines
Image of Accreting Giant
sallum+
IR band
LkCa15A
Central Star 10
Flux (mJy) 1
0.1
Wave length (μm)
Estimated emission
from accreting disk L’ Ks Hα
Where it comes from?
Estimated emission
from accreting planet
Star IR disk Ha / points lines explain origin
To begin with the background.
This is one of the results of direct-imaging of young star system.
At the center of this figure, the proto-star LkCa15A is masked.
Each color in this figure means photon detection. Red and Green means IR band L' and Ks respectively.
Since LkCa15 system is very yang, so these photon sources are thought to be the accreting planets in the gaseous disk.
The inner one, LkCa15b, is also detected in the H-alpha line, namely hydrogen Balmer-alpha.
The right figure is the Spectral Energy Distribution of these planets. Horizontal axis is the wave length and vertical axis is the energy flux.
The 3 color dots are the observational points, and the two lines are the theoretical estimate of the energy flux of plants.
Black one corresponds to the accreting disk and pink one corresponds to the accreting planet.
Of course depends on the model parameters, these theoretical estimate seems to be able to explain the observational points in IR.
However, the blue dots, namely H-alpha is far from these model lines.
IR emission
Hα line
⇒can be explained
⇒is never explained

3. 1-2. Black-body temperature
Heating process
viscous heating
shock heating
⇒ release of gravitational energy
Cooling by the black body radiation
That Spectral Energy Distribution bases on the black body radiation.
In the accreting planets, main heating processes are viscous heating and shock heating.
But both of them can be interpreted as the release of gravitational energy.
So when we assume the black body cooling, we can get an equation.
And when we substitute model parameters, we can get gas black body temperature as about 10^3 K.
So basically, the previous Spectral Energy Density is about black body radiation of a thousand K.

4. 1-3. Line emission Hα Lyα Collision
(observed in LkCa15b)
・・・
・・・
quantum number
Principal
n=4
n=3
Collision
free electron
n=2
n=1
ground state
On the other hand, let me touch on the line emission.
Here, I illustrate the energy levels as the blue bars.
Each lines represent each energy level, whose principal quantum number is 1, 2, …
The most bottom one is ground state, and almost all hydrogen is there in low temperature.
As you know, the hydrogen lines are emitted with the spontaneous de-excitation from higher level of hydrogen to lower level.
E.g. 2 to 1 de-excitation produce the Ly alpha photon, and 3 to 2 does the H alpha photon, that is the observed one.
So the excited hydrogen is needed to emit hydrogen lines.
Usually, such excited hydrogen is generated by collision with the free electron.
And the energy differences between hydrogen energy levels are about 10eV or 10^4 K.
So the strong Halpha line emission needs high temperature, typically larger than 10^4 K.
On the other hand, as I showed in previous slide, black body radiation of 10^3 K can explain the IR observation, well.
Therefore we need 2 different temperature in order to explain both of the H-alpha and IR emission.
Line emission needs much high temperature (>104K)
IR emission means lower temperature (<103K)

5. 1-4. Shock with Vertical Inflow
Tanigawa+2012
edge on
In order to explain these, we focus on shock heating with vertical inflow like this.
This is the schematic illustration of accreting gas giants based on a 3D hydrodynamic simulation of Tanigawa+2012.
This is the edge on figure of CPD.
The gas in the mid-plane of CSD cannot flow into the CPD, directly.
Because of the strength of gravitational barrier, the gas accrete from higher altitude of CSD to the CPD in vertical direction.
This vertically accreting gas release the gravitational energy at once on the surface of the CPD or plant. Thus, very strong shock front appears and the gas temperature can reach very high, hotter than 10^4 K, near the planet.
Then such hot gas can emit strong hydrogen lines.
But hydrogen line emission means hydrogen line cooling occurs in the high temperature region.
And in the vertical accretion flow, the heating occurs only once at the shock front,.
So after the shock heating, the gas cools monotonically.
When this hot gas cools rapidly, such hot gas hardly affects the IR continuum because of their optically thinness.
Therefore, the hot line emission and warm IR continuum can be explained at the same time.
Planet
Gas temperature reaches >104K near the planet.
When this hot gas cools rapidly, hardly affects IR continuum.

6. 1-5. Purpose of this Study
To understand how Hα line is yielded around accreting gas giant.
To estimate intensity of Hα line emitted from vertically accreting gas flow.
To constrain the gas giant forming condition by using observed Hα line.
Here, We show the purpose of this study.
We want to understand how to yield the H-alpha line around the accreting gas giant.
And we want to estimate intensity of H-alpha line emitted from the vertically accreting gas flow, in quantitatively.
And then, if we can, we want to constrain the gas giants forming condition by using these observed H alpha line emission.

7. numerically calculate the flow after the shock
2. Model
continuous flow
cooling
(including Line cooling)
vertically accreting
shock heating
initial parameters
v0: gas velocity
n0: gas number density
numerically calculate
the flow after the shock
Considered processes
I show our model of this study.
The vertically accreting gas hits on the surface of CPD, and is heated by the strong shock.
In this study, we numerically treat only the post shock region, because cooling region corresponds the line emitting region.
For simplicity, we assume 1D flow and continuous flow.
Actually, the initial parameters are three, pre-shock gas velocity and pre-shock gas number density, and pre-shock pressure. But we assume the strong shock and then, the pre-shock pressure is not important. So these two are the initial parameters.
In our numerical model, we consider the hydrodynamics, chemical reactions, electron tranistions, and radiative transfer.
Hydrodynamics
Chemical Reaction
Electron Transition
Radiative Transfer
assuming 1D flow
33 chemical species composed with H, He, C, O
10 electron levels and ion state of hydrogen
emission and absorption of 55 lines and continuum of H

8. ⇄ depth from shock surface
3-1. Temperature
v0=40km/s
n0=1017m-3
shock
surface
t=0
10-7
10-6
10-5
time(s)
10-4
⇄ depth from shock surface
10-3
~10-3s
10-2
I’ll show some figures in order to share the image of post shock region.
This is the temporal change of temperature. vertical axis is the time and horizontal axis is the temperature.
After here, we use 40km/s for preshock velosity, and 10^17m-3 for the pre-shock gas number density. as the initial parameters.
At just after the shock heating, the gas temperature reaches 6*10^4K in this initial parameters.
And then, the gas cools to 1000K in about 1s, mainly with two cooling processes
Though I show the temporal changes, but you can easily interpret this vertical axis into the distance from the shock front, by times the gas velocity.
The gas is in sub-sonic velocity, namely about 10km/s.
So 1s, the bottom of this figure, corresponds to the 10km from shock front, and in the column density, 1s corresponds to 10^21 m^-2.
Thus hot gas but only in thin region seems to be achieved.
10-1
~1s 1
103
104
105
　Temperature
(K)

9. 3-2. Chemical species H2O H H2 OH CO H+ e- State of Hydrogen H2 H H+zz
v0=40km/s
n0=1017m-3
10-7
State of
Hydrogen
H2O H H2
10-6 OH
10-5 H2
time (s)
10-4
~10-3s
10-3 CO H
(~100%)
10-2 H+
Next, we show the chemical abundance after the shock front.
The vertical axis is also time and horizontal axis is the relative chemical abundance to proton. And for your reference, I also show the temperature profile at right. this is same as the previous figure.
At first, since we assume molecule hydrogen comes into the shock front, all hydrogen in in the molecular form, and thus the H2 is in the 0.5 in this figure.
And then, we can see the hydrogen dissociate to atomic hydrogen in 10^-3 s time scale. This can be seen in temperature profile as the first steep drop.
And then, the atomic hydrogen is ionized in 10^-2 or so time scale.
In this parameters, because of lower shock velocity, the ionization rate is only about 10%. e-
10-1
~10-2s H+
(~10%) 1
10-6
10-4
10-2 1 5 10
ratio to H
Temperature
(104K)

10. 3-3.Line Enery Flux v0=40km/s n0=1017m-3 Hα Lyman α Paschen α
10-7
10-6 Hα
10-5
Lyman α
Paschen α
10-4
radiation
upward
time (s)
10-3
10-2
10-1
Now, let me show the line energy flux, the main topic of this study.
In this figure, the vertical axis is also time, and horizontal is the energy flux. The right figure is also temperature.
But please see this left figure from down to up, because I show the upward radiation flux. In other wards, this is the flux of the photon emitted in deeper region and goes through the shock front, and goes away. And can be observed.
We can see the hydrogen line is emitted in the second temperature dropping region. As we see previous figure, this is the hydrogen ionizing region, namely the hydrogen exciting region.
the black line corresponds to the Lyman-alpha, and red and blue corresponds to Ha and Pa respectively.
#From this figure, all three lines seems to become strong monotonically, from dwon to up.
And now, we got the energy flux of Hydrogen lines at the shock front.
So by using some circum planetary disk model, we can get the luminosity of hydrogen lines from around accreting gas giants.
#However, before that, let me touch on the absorption of lines.
100
101 2 5 10
10-4
10-1
102
105
Energy flux (W/m2)
Temperature
(104K)

11. 3-4.Hα Intensity with v0 r CPD v0 v0 (km/s) Free fall 5 1020 m-3
log(Energy flux)
(W/m2)
1017 m-3 r -1 v0
1016 m-3 -3
Then, this figure shows the results of parameter study for the 2 initial parameters. preshock velocity and preshock gas number density.
The horizontal ~
The vertical ~
Each colors corresponds to each pre-shock gas number density.
Now, we assume the pre-shock velocity is about free fall velocity. This is not so bad according to 3D-hydrodynamic simulation.
Then, Our initial parameter v0 can be interpreted into the radial distance from the forming planet.
And we also assume that gas density is constant on the line emitting region.
The line emitting region is not so large.
Since strong line emission needs the strong shock, we treat only the region very close to the planet. (roughtly 10 jupiter radius. about 30 or 40 km/s is the critical)
So we can integrate the energy flux in the radial distance direction, (which corresponds to the v0 integration).
Thus, we get the luminosity of hydrogen line from around the accreting planet including the CPD surface.
1015 m-3 -5 10 30 50 80
v0 (km/s)

12. 3-5. Hα Luminosity log(n0)(m-3) Planet mass (Mj) 1 10 20 19 18 17 16
This counter is the results of the H alpha line flux integration.
The vertical axis corresponds the the gas number density, and the horizontal axis corresponds to the planet mass.
Each black line is the counter of the H alpha luminosity. the most left bottom lines corresponds the the 10^16W and the most right top lines corresponds to the 10^24 W
So now, we have a luminosity for each planet mass and accreting gas density. 15 1 10
Planet mass (Mj)

13. 4-1. LkCa15b log(n0)(m-3) Planet mass (Mj) 1023W LkCa15b 1017W 1 10 2019
LkCa15b
2.2×1022 W
LkCa15b 18
MMSN
(12.6AU)
log(n0)(m-3) 17 16
1017W
For a discussion, we draw the additional red line in the H alpha contour.
This red one corresponds to the LkCa15b’s H alpha line luminosity.
And this pink line corresponds the MMSN gas density for 12.6AU. I show this only for the reference value.
I never claim that this gas density can apply to the LkCa15b, but this is one of reference value I think.
When the 10Mj planet is embedded in the MMSN at 12.6AU, then Ha emission of LkCa15b can be explained. 15 1 10
Planet mass (Mj)

14. Summary Background Purpouse Method Result Conclusion
Recently, some forming gas giants have been observed.
How Hα line is yielded is yet understood.
To explain the Hα line intensity of LkCa15b
To constrain the condition of gas accretion
We numerically calculate radiative cooling with 1D flow, chemical reaction, electron transition, and radiative transfer.
Hα line intensity from shock heated gas is strong enough to be observed.
By using our model, Hα line intensity constrains the planet mass and gas number density.
Purpouse
Method
Let me summarize this talk
Origin of H-alpha is yet to be
Result
Conclusion