The $r$-process and sensitivities to nuclear physics

Matthew Mumpower

Los Alamos National Lab

ICNT: $r$-process workshop

Monday June 6$^{th}$ 2016

The $r$-process and sensitivities to nuclear physics

Matthew Mumpower

Los Alamos National Lab

ICNT: $r$-process workshop

Monday June 6$^{th}$ 2016

Last Week

Tuesday: $r$-process in SN & NS mergers; kilonovae

Wednesday: Gravitational waves and observations

Thursday: GCE & new fission results

Friday: Nuclear structure and recent measurements

We need to do this more often &... these problems are hard!

A focused, cross-discipline approach is warranted

Review Paper

The impact of individual nuclear properties on $r$-process nucleosynthesis

Mumpower et al. PPNP 86 86-126 (2016)

Figure: Experimental reach of future radioactive beam facilities

Interactive data tables can be found online: MatthewMumpower.com

Motivation

Ultimately... we want to know what is the site of the $r$-process?

What do we currently know on the nuclear physics side?

What is most important nuclear physics for late-times in the $r$-process?

How well can we currently predict final abundance patterns?

What do we need to measure?

How do these measurements help us to move forward?

On the astrophysics side

We heard a lot about this last week...

Entropy or $S$

Timescale or $\tau$

Neutron-richness or $Y_e$

Ejected mass or $M_{ej}$

A key metric: Neutron-to-seed ratio ($R$)

Stages of the $r$-process

Figure by A. Arcones (2011)

The importance of the freeze-out phase

Freeze-out is the last phase of the $r$-process when nuclides decay back to stability.

Individual rates and properties become critical to the evolution as nuclei fall out of equilibrium.

In order to accurately predict $r$-process abundances it is imperative to understand how these nuclear inputs evolve with neutron excess.

During Freeze-out ($R\lesssim1$)

Two types of evolutions

Hot

  • Classical $r$-process with high $T_9$
  • Long phase of $(n,\gamma)\rightleftarrows(\gamma,n)$

Cold

  • Short or nonexistent $(n,\gamma)\rightleftarrows(\gamma,n)$
  • Quasi-equilibrium neutron capture & $\beta$-decay

Inputs from nuclear physics

1st order: masses, $\beta$-decay rates, reaction rates & branching ratios

What do we know?

The chart of nuclides

What do we know?

All half-lives

What do we know?

Recently measured beta-decay half-lives

What do we know?

Recently measured beta-decay half-lives

What do we know?

Nuclear masses

What do we know?

Neutron capture rates

What do we know?

As of today, to varying degrees of accuracy

What do we know?

So we must rely on theory... even with FRIB

What do we know?

So we must rely on theory... even with FRIB

$r$-Process Calculation

PRISM: Portable Routines for Integrated nucleoSynthesis Modeling

Trevor Sprouse (Notre Dame)

Movie time!

Motivation

Ultimately... we want to know what is the site of the $r$-process?

What do we currently know on the nuclear physics side?

What is most important nuclear physics for late-times in the $r$-process?

How well can we currently predict final abundance patterns?

What do we need to measure?

How do these measurements help us to move forward?

How do we assign error bars?

One method is to use Monte Carlo calculations

  1. Allow the uncertain nuclear input to vary
  2. Produce an abundance pattern with varied dataset
  3. Repeat many times to create ensemble
  4. Combine the ensemble of abundance patterns

masses $\Delta\sim500$ keV (or more!)

$\beta$-decay rates $\Delta\sim2$ to $10$

neutron capture rates $\Delta\sim10$ to $1000$

Mass models predictions

Towards the neutron-dripline mass model predictions diverge

Tin (Z=50) & Europium (Z=63) isotopic chains

masses $\Delta\sim500$ keV (or more!)

Mumpower et al. PPNP 86 86-126 (2016)

Error bars from masses

Hot wind: $S\sim200$, $\tau=80$ ms, $Y_e=0.3$

Mumpower et al. PPNP 86 86-126 (2016)

Error bars from masses

Hot wind: $S\sim200$, $\tau=80$ ms, $Y_e=0.3$

Rule of thumb: $\Delta_\text{mass}\sim500$ keV $\Rightarrow$ $\Delta_Y\sim 2-3$ orders of magnitude

Mumpower et al. PPNP 86 86-126 (2016)

$\beta$-decay preidictions

$\beta$-decay rates $\Delta\sim2$ to $10$

Mumpower et al. PPNP 86 86-126 (2016)

Error bars from $\beta$-decay

Hot wind: $S\sim200$, $\tau=80$ ms, $Y_e=0.3$

Rule of thumb: $\Delta_{\beta}\sim10$ $\Rightarrow$ $\Delta_Y\sim 1-2$ orders of magnitude

Mumpower et al. PPNP 86 86-126 (2016)

Neutron capture preidictions

Evaluated at $T_9=1.0$

Tin (Z=50) & Europium (Z=63) isotopic chains

neutron capture rates $\Delta\sim10$ to $1000$

See Stylianos' talk later in the week

Mumpower et al. PPNP 86 86-126 (2016)

Error bars from neutron capture

Neutron star merger $r$-process

Reduction in uncertainties from light to dark shading

Rule of thumb: $\Delta_{n,\gamma}\sim100$ $\Rightarrow$ $\Delta_Y\sim 1-2$ orders of magnitude

Liddick et al. PRL to be published (2016)

The Rare Earth Peak

The Rare Earth Peak (REP)

We seek to understand the formation of this abundance feature

Sensitive to both astrophysical conditions & nuclear physics input

Proposed ways to form the REP

  1. Dynamical formation during freeze-out ($R\lesssim1$)
    Requires a localized nuclear structure effect (kink)
  2. Via fission fragment yields
    Requires dumping heavy products in exactly the right spot

Formation of REP

Hot wind: $S\sim200$, $\tau=80$ ms, $Y_e=0.3$

M. Mumpower et al. PRC 85 045801 (2012)

Formation of REP

Cold wind: $S\sim300$, $\tau=80$ ms, $Y_e=0.4$

M. Mumpower et al. PRC 85 045801 (2012)

Failure of REP Formation

Using the ETFSI-Q mass model

M. Mumpower et al. PRC 85 045801 (2012)

Successful REP Formation

Using the FRDM95 mass model

M. Mumpower et al. PRC 85 045801 (2012)

A focused, cross-discipline approach...

The Rare Earth Peak

Turn the problem around

Try to constrain nuclear physics with obs. & exp.

Method 1 is testable...

  1. Dynamical formation during freeze-out ($R\lesssim1$)
    Requires a localized nuclear structure (kink)
    Relatively few nuclei to measure
    Hints from Jin Wu's $T_{1/2}$ measurements
    Very close to making necessary mass measurements (FRIB & other facilities)
  2. Via fission fragment yields
    Requires dumping heavy products in exactly the right spot
    Extreme $r$-process conditions necessary
    Need to make measurements on hundreds of the heaviest nuclei
    Problem: We can't reach these nuclei, even with FRIB

Reverse Engineering Masses

  • Fix the astrophysical conditions (hot, cold or merger)
  • Use the Metropolis algorithm: at each step the parameters of the mass model are varied
  • Update all nuclear properties self-consistently
  • Use abundances, which are well known, (calculate the Likelihood function) to determine if the step was successful



$L\sim$ match red abundances
M. Mumpower et al. arXiv:1603.02600 (2016)

First attempt

Hot wind $r$-process with default DZ parameters

Success?! But there's a problem!

M. Mumpower et al. arXiv:1603.02600 (2016)

First attempt

Hot wind $r$-process with new DZ parameters

Success?!... But there's a problem!

M. Mumpower et al. arXiv:1603.02600 (2016)

Didn't match known masses

We need to tell the Metropolis algorithm to match both

Update Likelihood function:

$L\sim$ match abundances + match known masses

M. Mumpower et al. arXiv:1603.02600 (2016)

Results with DZ alone

No combination of DZ parameters can simultaneously reproduce the rare earth peak and match the known masses at the same time

The nuclear structure information responsible for the rare earth peak is missing from the model

We could move to a nuclear model, but these are more complicated to analyze, with many coupled parameters.

The benefit to DZ is that the abundances are flat to start with.
Let's try to add the missing physics!

M. Mumpower et al. arXiv:1603.02600 (2016)

Parameterize missing physics

$M(Z,N) = M_{DZ}(Z,N) + $$a_N$$ exp[-(Z-$$C$$)^2/2$$f$$]$

$a_N$ - Strength of change for given neutron number in MeV

$C$ - Center of the distribution in proton number

$f$ - Rate of fall off back to stability

Now we repeat the Monte Carlo calculations, letting these parameters vary

M. Mumpower et al. arXiv:1603.02600 (2016)

Results with new parameters

The predicted masses for $Z=60$ (Nd)

Distinguishable predictions given different astrophysical conditions

Hot: local min even-N • wider in N • smaller change to masses

Cold: local min odd-N • tigher in N • larger change to masses

M. Mumpower et al. arXiv:1603.02600 (2016)

Evolution of Abundances

Before • During • After peak formation

Great success! Difference is encoded in the astrophysical conditions

M. Mumpower et al. arXiv:1603.02600 (2016)

Masses: combining conditions

Similar hot & cold conditions

M. Mumpower et al. arXiv:1603.02600 (2016)

Abundances: combining conditions

Similar hot & cold conditions

M. Mumpower et al. arXiv:1603.02600 (2016)

Reverse Engineering Masses

What are the consequences of the future measurements?

Either we find the structure... or we don't

If we do: we favor precise conditions for the main $r$-process

If we don't: we favor extreme conditions that REQUIRE fission recycling... our only option at the moment is mergers

Perhaps nature is more complicated than we think... and we learn something even more profound

Go make the measurements to find out!

$\beta$-Oslo Method

Accepted to PRL - Liddick et al. (2016)

Neutron capture measurements far from stability are challenging

Constrain $^{69}$Ni(n,$\gamma$)$^{70}$Ni by populating $^{70}$Ni via $\beta$-decay of $^{70}$Co

$\beta$-Oslo Results

Accepted to PRL - Liddick et al. (2016)

Neutron capture measurements far from stability are challenging

Constrain $^{69}$Ni(n,$\gamma$)$^{70}$Ni by populating $^{70}$Ni via $\beta$-decay of $^{70}$Co

Figure: (a) level density (b) $\gamma$SF (c) reduction in rate uncertainty

To be featured as PRL Editors' Suggestion

$\beta$-Oslo Future Application

Accepted to PRL - Liddick et al. (2016)

Suppose we apply this method to many neutron-rich nuclei...

Reduction in uncertainties from light to dark shading

Neutron-gamma competition

Spyrou et al. submitted (2016)

Use the same experiment to study neutron emission from $^{70}$Ni

Theory: Where are we going?

Recently completed fission barrier heights

In the works at Los Alamos: fission fragment yields, neutron-induced fission reaction rates, and $\beta$-delayed fission probabilities

P. Möller & M. Mumpower et al. (2015)

Special thanks to

My collaborators

G. C. McLaughlin, R. Surman, A. Aprahamian, M. Beard, I. Bentley, S. Marley, P. Möller, D.-L. Fang, A. W. Steiner, T. Kawano, S. Liddick, A. Spyrou & T. Sprouse

Summary

Right now predictions of final $r$-process patterns are shrouded by large uncertainties.

However, targeted experimental campaigns, e.g. in the rare earth region, will help to further constrain nuclear models.

This does not necessarily mean improved predictive power for nuclear models.

We have to learn how to draw conclusions, although models (and data in some cases) are imperfect.

One thing is certain: We can continue moving forward by working together!