1. PRE(Photospheric Radius Expansion) X-ray burst simulation with MESA(Modules for Experiments in Stellar Astrophysics)
rd CHEA Workshop
Gwangeon Seong
Good afternoon, my name is Gwangeon Seong, a graduate student of Computational Astrophysics Lab. I am very honored to have the opportunity to present here. I’m going to talk about the Photospheric Radius Expansion X-ray burst simulation with Modules for Experiments in Stellar Astrophsycis.

2. MESA
An open source code for 1-D stellar evolution (Paxton et al. 2011). MESA combines many of physics modules for simulations of stellar evolutions.
Hydrodynamics
First of all, I want to introduce the code used in my research. The name of the code is MESA, an open source code for 1-D stellar evolution. This combines many of the numerical and physics modules for simulations of the stellar evolution, but it is designed to applied to a wide range of stellar physics applications. The wide range of stellar evolution scenarios from very small mass to high mass and advanced evolutionary phases can be treated with many physical inputs, like the equation of state, opacities, and nuclear reaction network.
Mixing
Equation of state
Nuclear reaction
Opacities

3. Simulations of Type I X-ray bursts
MESA paper 3
Initial neutron star model
ns_relax.mod (M = 1.4 solar mass, R = 11.2km)
Accretion composition
Constant accretion rate
Reaction network (rp-process)
Of course, MESA can do modeling of X-ray bursts. This is done by choosing the inner boundary as the surface of Neutron star and adding the accretion process. For a given surface, MESA adds accretion materials onto the surface at each time step which is determined by the accretion composition and the accretion rate. Then, the energy is generated by rapid proton capture process and by solving the equations, MESA can predict the lightcurves of X-ray burst.

4. PRE bursts
In some type I X-ray bursts, the luminosity reaches the Eddington limit.
The surface temperature drop
Photosphere expansion
Photospheric radius decrease
High radiation pressure
An example of a typical X-ray burst simulation is introduced in the test suite of the MESA code, but it is not a photospheric radius expansion X-ray burst. Photospheric radius expansion(PRE) means, in some XRBs, the energy of radiation is large enough that the luminosity reaches the Eddington limit, so the photon pressure is large enough to push out the photosphere. When this condition met, the photosphere expands by the radiation pressure and thus this phenomenon is called photospheric radius expansion. Then, by the expansion, the surface temperature is lowered, and the nuclear reaction does not occur. Then the radiation pressure decreases, causing the surface to shrink.

5. PRE bursts
Here is the observation for the PRE burst. Two models circled in red are PRE bursts. For these models, the luminosity, temperature, and radius figure show that the photosphere expands due to radiation pressure and the temperature drops due to the expansion.

6. Simulation Hydrodynamics Mixing Equation of state Nuclear reaction
Opacities
So, the purpose of our research is to model PRE XRBs using MESA code, and to find the condition that causes the PRE phenomenon. In order to do that, we first tried to change the nuclear reaction, one of the physical inputs of MESA. In this simulation, this input consists of the reaction rate, the reaction network and Accretion composition. Here are some models that apply these changes.
Reaction rate
Reaction network
Accretion composition

7. Models Reaction rate Accretion composition : H : 70.48% , He : 27.52%,
Z = 2%
Reaction network
: rp_53
First, we changed the reaction rate. Figure 1 is the light curve of the XRB model given by test suite of MESA code. The conditions used in this model are the accretion rate M_dot is 3 times 10 to the -9 solar mass/ year, the reaction rate is rp53 which contains 53 nuclei and following accretion composition. black line is Eddington luminosity of the log scale, and red line is the total luminosity of the log scale. Figure 2 shows the model in which only the accretion rate is changed to 5 times 10 to the -9 solar mass/year in Figure 1. As you can see, the result is that the accretion rate cannot change the shape of the lightcurve and the luminosity, but only can change the explosion period called recurrence time.
Figure 2. (Accretion Rate Ṁ=5 × 10⁻⁹M⊙ /year)
Figure 1. Reference model (Accretion Rate Ṁ=3 × 10⁻⁹M⊙ /year)

8. Models Reaction network (b) (d) (c)
Figure 3. (Reaction network : rp_305)
Reaction network
(b)
Second, Figure 3 shows the model in which only the Reaction network is changed to rp305 which contains 305 nuclei in the reference model. Red line is the Eddington luminosity of the log scale, and black line is the total luminosity of the log scale. B, c and d are the light curve, radius, and effective temperature that rescale the time axis. The total luminosity at the peak point approaches Eddington luminosity, but according to the radius and the effective temperature figure, this model does not represent the PRE.
(d)
(c)
Figure 1. Reference model (Reaction network : rp_53)

9. Models Accretion composition Reaction network : rp_305 Accretion Rate
: Ṁ=3 × 10⁻⁹M⊙ /year
Accretion composition
The last model Figure 4 shows the model that changes the accretion composition of figure3 to be composed of helium only. The total luminosity of this model is seen to exceed Eddington luminosity, but in this situation the simulation does not proceed because the timestep determined at the point where the luminosity goes beyond the Eddington luminosity is too short. We have simulated using several different models such as a model with 50% helium and 50% hydrogen, but if the luminosity exceeds the Eddington luminosity, the same problem continues to occur. But according to the result, we can see the accretion composition plays an important role in increasing the luminosity. Therefore, in order to further study, we are trying to solve this timestep problem.
Figure 3. (Accretion composition : H : 70.48% , He : 27.52%, Z = 2%)
Figure 4. (Accretion composition : H : 0% , He : 100%, Z = 0%)

10. Summary and Future work
MESA can do modeling X-ray bursts by using the accretion process.
The reaction network and the composition of the accretion materials play an important role in the modeling PRE XRBs.
If the luminosity goes beyond the Eddington luminosity, the simulation does not proceed because of the timestep problem.
To solve this problem, we will look for the cause of the problem and find a solution.
By changing the model parameters, we will investigate systematically the conditions that can cause PRE phenomenon.
Let me summary my presentation.
MESA code can do modeling X-ray bursts by using the accretion process.
Nuclear reaction which is the one of physical inputs of MESA plays an important role in the modeling PRE XRBs. Especially, The reaction network and the accretion composition are very important factors to increase luminosity.
But, If the luminosity goes beyond the Eddington luminosity, the simulation does not proceed because of the timestep problem.
그리고 뒤로 읽자.

11. Thank you for listening