The asteroseismic imprints of mass transfer on an accretor star
Interactive version of plots from Wagg+2024
This page is an interactive version of some of the plots from my paper Wagg+2024, which investigates the asteroseismic imprints of mass transfer on an accretor star. We used MESA and GYRE to simulate the asteroseismic signals from a $3.0 \, \rm M_\odot$ star that accretes $0.5 \,
\rm M_\odot$ from a companion star.
Below you can explore some of our main results interactively and learn about the evolution and asteroseismic signals from our accretor star model. If you'd like to reproduce any of the results or plots from our paper, our inlists, scripts and data are available on GitHub and Zenodo.
What am I looking at: In the plot below I show the Hertzsprung-Russell diagram for both the donor and accretor star in my models (see Fig. 1 in the paper). The accretor track is outlined in green and both tracks are coloured by the rate of mass transfer. Note that this plot shows the full evolution of the donor when we allow it continue mass transfer in its entirety, but for the paper we end mass transfer once $0.5 \, \rm M_\odot$ has been accreted.
How can I interact with it: You can pan and zoom across the plot, as well as hover over individual points to see the values of $L$, $T_{\rm eff}$, $\dot{m}$ and $t$ (I recommend looking at the times to see that most of time is spent is a relatively small area on this plot!). Additionally, the "Key evolution points" buttons will move the red markers to help guide your eye to where certain events occur.
Where can I read more: For more information explaining this plot in detail check out Section 3.1 of the paper!
Click on the buttons to see where the stars are in the HRD at different key points in their evolution.
What am I looking at: The two plots below show evolution of the internal structure of a mass-gainer (accretor), which starts as a $3.0 \, \rm M_\odot$ star and accretes $0.5 \, \rm M_\odot$, compared to that of a single star with the same final mass ($3.5 \, {\rm M_\odot}$). The left plot shows the hydrogen abundance profile, which tells you how the composition of the star changes throughout. The right plot shows the Brunt-Väisälä frequency, $N$, which is a measure of convective instability and directly determines the period distribution of $g$ mode oscillations in the star.
How can I interact with it: As above, you can pan around the plot and zoom in. You can also toggle which lines to show by clicking their labels in the legend. In addition, you can use the buttons below to animate the plot (and change the speed of animation), or alternatively use the slider to hop around to specific times. For reference, the mass transfer occurs around 162 Myr (you'll notice the time resolution gets much finer there).
Where can I read more: For more information explaining these plots in detail check out Section 3.2 and 4.1 of the paper!
There's a lot of information to unpack in these internal structure plots - let's try stepping through them in detail with some questions about each, ordered approximately chronologically.
Nuclear fusion! Fusion in the core of the star converts hydrogen into helium, which causes the abundance of hydrogen to decrease at the centre.
Since the core of this star is convective, the hydrogen abundance is uniform in the core and you see an extended region decrease in abundance over time.
The core is contracting! As the star evolves, the core contracts (in mass coordinate) and the region of uniform abundance shrinks.
This is because the reduced abundance in the core decreases its opacity, allowing radiation to travel more freely and ending convection at a lower mass coordinate.
Did you notice that as the core recedes it leaves a chemical composition gradient behind (the diagonal line in the profile)? That'll be important later!
They have different masses! A more massive star evolves faster and the single star is initially $0.5 \, \rm M_\odot$ more massive than the mass-gainer. You'll note they also have different size cores for the same reason.
The star's luminosity increases! As the star gains mass, its luminosity increases, which causes the region of convection to expand in mass coordinate through the star.
This is rejuvenation! As the core expands due to accretion, it mixes in the more hydrogen-rich material outside the core and increases the abundance in the core. This effectively "rejuvenates" the star and extends its lifetime.
If you're interested in looking into some of the first rejuvenation investigations you could read Neo+1977 or Hellings+1983.
Diffusive mixing! Over time, the kink in the profile is smoothed out by diffusive mixing after accretion - though it sticks around all the way until the end of the main sequence!
This kink is a long-lived signature of mass transfer that ends up directly affecting the asteroseismic signals.
This is the convective core! The Brunt-Väisälä frequency defines the frequency at which a small element of vertically displaced material will oscillate within a radiative region.
This means it is not defined in convective regions (where a small element but not oscillate but instead keep moving upwards), so the absence of a value towards the centre indicates the presence of a convective core.
The chemical composition gradient! If you look at the abundance profile you'll see that the peak in the Brunt-Väisälä frequency is at precisely the same mass coordiantes as the chemical composition gradient (diagonal part of the line) that is left behind as the core recedes.
For an ideal gas, the Brunt-Väisälä frequency is given by $$ N^2 = \frac{g^2 \rho}{P} (\nabla_{\rm ad} - \nabla + \nabla_\mu) $$ where $g$ is the acceleration due to gravity, $\rho$ is the density, $P$ is the pressure, $\nabla_{\rm ad}$ is the adiabatic temperature gradient and $\nabla \equiv \frac{d \ln T}{d \ln P}$ is the temperature gradient and $\nabla_\mu \equiv \frac{d \ln \mu}{d \ln P}$ is the chemical composition gradient.
So as the $\nabla_\mu$ term increases, so does the Brunt-Väisälä frequency.
It's a signature of accretion! The kink in the abundance profile is a long-lived signature of mass transfer and, since the Brunt-Väisälä frequency is sensitive to the chemical composition gradient, it is also sensitive to the signature.
Keep reading to see how this affects the asteroseismic signals!
What am I looking at: The plot below shows the period spacing pattern for the mass-gainer and single star. This shows the spacing between the periods of consecutive $g$ modes in the star, which is sensitive to the Brunt-Väisälä frequency and hence the internal structure of the star. This is a key observable in asteroseismology and is used to infer the internal structure of stars.
How can I interact with it: As above, you can pan around the plot and zoom in. You can also toggle which lines to show by clicking their labels in the legend. In addition, you can use the buttons below to switch the central hydrogen abundance and see how the pattern changes over time.
Where can I read more: For more information explaining this plot in detail check out Section 4.2 of the paper!
Click on the buttons to see how the period spacing pattern changes with the central hydrogen abundance.
The buttons are separated slightly to highlight where accretion occurs.
This is similar to seeing how the pattern evolves over time, but allows a consistent comparison between the single star and mass-gainer.
The stars have different convective core sizes! Before accretion, the single star is $0.5 \, \rm M_\odot$ more massive and so has a larger convective core. The asymptotic period spacing is defined as $$ \Delta P = \frac{2 \pi^2}{\sqrt{l(l+1)}} \int_{r_1}^{r_2} \frac{N}{r} \, dr $$ where $N$ is the Brunt-Väisälä frequency, $l$ is the degree of the mode, $r$ is the radius and the integral is over the radiative region of the star (set by $r_1$ and $r_2$). A different convective core size alters $r_1$ and hence the asymptotic period spacing.
It's the chemical composition gradient! Any abrupt shifts in the Brunt-Väisälä frequency profile trap particular modes in certain regions of the star, altering their periods relative to the regular pattern.
Remember from the section above that the Brunt-Väisälä frequency is sensitive to the chemical composition gradient, so any changes in the gradient will affect the period spacing pattern in this way. Therefore, we see more modes trapped over time as the chemical composition gradient develops over the star's main sequence.
It's a signature of accretion! The kink in the abundance profile is a long-lived signature of mass transfer and, since the period spacing pattern is sensitive to the chemical composition gradient, it is also sensitive to the signature.
As we saw in the internal structure plots, this feature remains present until the end of the main sequence. You can also see (maybe focus on $X_c = 0.1$) that only a subset of the modes actually end up out-of-phase, whilst others lines up quite well. That's because the mass-gainer profile is only different from the single star in very specific locations and so only certain modes are sensitive to the differences.