Delayed and Displaced

The Impact of Binary Interactions on Core-collapse SN Feedback

Wagg et al. 2025

A brief overview

Welcome! You've found the page for the interactive plots for our paper about how binary interactions can delay and displace core-collapse supernova feedback.

What did we do? In this study, we used cogsworth to postprocess the FIRE m11h hydrodynamical zoom-in simulation and perform self-consistent population synthesis and galactic dynamics simulations. This allows us to evolve a large population of binaries through a galactic potential and track the precise times and locations are which the stars reached core collapse. We repeated these simulations for a range of different assumptions regarding binary physics, initial conditions and galaxy parameters.

What are our main results? We find that ~25% of supernovae occur more than 44 Myr after a star formation event. We also find that ~13% of supernovae explode more than 0.1kpc from their parent star clusters. These effects are both exacerbated in lower metallicity environments. We find that our results are mostly robust to uncertainties in binary physics and the other variations we considered, as you can explore below. We also created an analytic model for supernova feedback that can used in future models.

Why does this matter? Supernovae produce feedback in galaxies, which can inhibit further star formation. We find that feedback should extend over longer times and be spatially distributed to a greater extent than current feedback models. This may affect the evolution of galaxies, particularly those at high redshift since they are lower metallicity environments and much smaller.

How can I use this page? We have made several of the plots from our paper interactive to allow you to explore the full range of models that we explored. Each section below will explain the plot and how you can interact with it - enjoy!

Time-dependent spatial distributions Variations Summary plots Analytic model

Time-dependent spatial distribution of core-collapse supernovae

Figure 1

This section is an interactive version of the top right panel of Figure 1 from our paper. At first, this plot just shows the same fiducial population that you see in the paper (except you can zoom, pan and hover to get more information).

To start changing things, try switching between stacked and separate histograms to better understand how the different progenitor channels vary. You can also use the sliders and play/pause buttons to start imposing an upper limit on the timing of the supernovae. Finally, there's a list of all of the models that we ran that you can switch between to see how the distribution varies.

SN times < 4 Myr

Fiducial model trends

So let's first consider just the fiducial model and try to understand some of the variations that we see. Click each of the following dropdowns to find out the answers - the first couple focus on distances and the later ones bring in the time dependence too.

They live longer! The distances travelled by merger products and primary stars are both driven by the initial cluster velocity dispersion (which is $v_{\rm disp} \approx 1.7 \, {\rm km/s}$ in our fiducial model).

However, merger products tend to live much longer than primary stars so they have longer to disperse from the cluster.

Many are ejected by their companions! In many cases, after a primary star reaches core collapse, the binary is disrupted. At this point the secondary is ejected with its pre-supernova orbital velocity, potentially travelling vast distances before exploding.

Single stars can't live that long and still reach core collapse! At the average metallicity of our fiducial model, a star needs around $7 \, {\rm M_\odot}$ to reach core collapse, which corresponds to a lifetime of around $44 \, {\rm Myr}$. Stars with lower masses live longer...but they don't produce supernovae!

There are still a few primary/secondary supernovae that occur after this time, but these have experienced mass transfer with a companion and so have slightly altered their nuclear timescales.

Mergers from lower mass stars take more time! Take, for example, two 5 solar mass stars. Neither will reach core collapse on their own, and each has a much lengthier main sequence lifetime than a more massive star. But if they are close enough in orbit, once one expands sufficiently they can merge, and produce a star massive enough to explode.

Since the main sequence lifetime of these stars is so much longer, the merger (and therefore, supernova) may not occur for many tens of Myr after the final primary/secondary star supernova.

Most distances are driven by initial velocity dispersions! Although a fraction of secondaries are ejected by their companions, most stars travel distances based on their initial velocities. This means that stars that live longer simply have more time to disperse from their cluster and increase the distance.

For more details about all of this, check out Section 3 of the paper :)

Differences across model variations

Now try playing around with some of the buttons for different models and see if you can understand some of the trends. Below I include just a couple of interesting ones from each category to keep things short but we explored the trends in every model in the paper.

More mass and angular momentum is lost from the system! Fully nonconservative mass transfer means that all mass donated by a primary star is immediately lost from the system rather than accreted by the secondary. As a result, secondaries are often not as massive as the fiducial model and as such, don't expand and cause a reverse mass transfer event, which would lead to a merger. This reduced expansion of many secondaries reduces the number of merger products.

The mass lost from the system also carries away angular momentum. The loss of angular momentum causes many binaries to tighten, increasing the orbital velocity of the system. Therefore, ejected secondaries are typically faster, thereby increasing the distance that they travel before reaching core collapse.

Stars need less mass to explode and expand less during their lives! At lower metallicity, the minimum mass required for a star to reach core collapse in the underlying stellar models is reduced. This lower limit allows less massive (i.e., more slowly evolving) stars to reach core collapse. These lower mass stars extend the tail of late supernovae.

Moreover, the lower radial extent of low metallicity stars means that they can detach from Roche lobe overflow at much smaller separations. Therefore, binaries are often tighter at the moment of a primary star's core collapse, increasing the ejection velocities of secondaries.

Their velocities are controlled by binary interactions! Secondary stars are mostly ejected from their binaries by companions, and as such their velocities are set by binary interactions, not the initial cluster velocity dispersion. As such, the distances that they travel are mostly independent of this parameter.

For more details about all of this and more, check out Section 4 of the paper :)

Variations of binary physics, initial conditions and galaxy parameters

Figures 4-7

This section has an interactive plot that combines the data from Figure 5-8 in the paper. You can hover over each bar to see the exact values, and click particular progenitors in the legend to toggle them. The buttons let you switch between the time and distance plots, as well as narrow down on particular types of variations.

Which percentiles do you want to see?

Which subset of variations?

Summary plots

Figures 12-14

This section contains the summary plots for the main trends across our model, which we discuss in Section 6 of the paper. These plots all have linked y-axes, so any zooming or panning will apply to all plots at the same time. Feel free to zoom in on the variations that you care most about! You can use the button below all three to reset their axes after zooming (or use the home button on each individual plot).

Medians

Tails

Totals

Analytic model

Figures 9 & 10

This section lets you interact with the analytic model that we designed to fit the timing and progenitor velocity distributions of supernovae. You can alter the metallicity using the slider below and see how things change.

If you're curious about the general definition of the model, you can unfold the dropdowns below to get some info (and check out the paper for the full defintions!).

The rate of core-collapse supernovae over time is a simple broken power law that has physically-motivated metallicity-dependent transition points.

$\frac{\mathcal{R}_{\rm CSSN}(t / { \, \rm Myr})}{{ \, \rm Gyr}{\rm \, M_\odot}} \equiv \begin{cases} 0 & t \lt t_1, t \gt t_6,\\ a_{i} (t / t_{i})^{\psi_{i}} & t_{i} \le t \lt t_{i + 1}, i \lt 5,\\ a_6 e^{-t / t_5} & t_5 \le t \lt t_6 \end{cases}$

where $a_i$, $t_i$ and $\psi_i$ are metallicity-dependent parameters defined in the paper

The velocities of progenitors is set by a variety of factors, based on whether they were ejected by their companion, and then whether they experienced mass transfer and what type. Unejected progenitors simply follow the initial cluster velocity dispersion:

$p_{\rm unejected}(v) = \frac{1}{\sigma^3} \sqrt{\frac{2}{\pi}} v^2 e^{-v^2 / (2\sigma^2)},$

For ejected systems, it's more complicated and the branching ratio between different mass transfer types varies with metallicity (see Eq. 8-11 in the paper). The distribution for each type of ejection is as follows though

$p_{\rm no MT}(v | Z) = \begin{cases} A v^{-1.8 + 0.5 \sqrt{|{\rm [Fe/H]}|}} & v_{\rm min} \le v \le v_{\rm max} \\ 0 & {\rm else} \end{cases}$

$p_{\rm MT,A}(v|Z) = \mathcal{N}(22 - 8{\rm [Fe/H]}, 6 - 3{\rm [Fe/H]})$

$p_{\rm MT, B/C}(v|Z) \propto \beta\left(\frac{v - v_{\rm min}}{v_{\rm max}}, 1.5 - 1.5 {\rm [Fe/H]}, 18 + 5 {\rm [Fe/H]}\right)$

$p_{\rm MT, CE}(v|Z) \propto \beta\left(\frac{v - v_{\rm min}}{v_{\rm max}}, 5 - 4 {\rm [Fe/H]}, 10\right)$

where $A$ is a normalization constant, $v_{\rm min} = 5 \, {\rm km/s}$, $v_{\rm max} = 100 \, {\rm km/s}$, $\mathcal{N}$ is a normal distribution, and $\beta$ is the beta function.

0.08

[Fe/H] = 0.08

Still craving more science?

Well, oh boy do I have a paper for you 🙃 Use the button below to go and read the full paper in detail!

Read the paper

A brief overview

Time-dependent spatial distribution of core-collapse supernovae

Figure 1

Fiducial model trends

Why do merger products travel further than primary stars?

What causes secondary stars to reach the largest distances?

We don't predict any primary or secondary supernovae after ~60 Myr, why?

So, how do merger products still explode at later times?

As the slider moves to the right, the distances increase. Why does more time cause most of the distribution to shift to larger distances?

Differences across model variations

Fully nonconservative mass transfer (beta = 0) reduces the number of merger products, and makes secondary star supernovae more distant - why?

At low metallicity, why do supernovae occur later and at larger distances?

Why are secondary stars insensitive to reductions in the initial cluster velocity dispersion?