Reverse engineering nuclear properties from $r$-process abundances

Matthew Mumpower

Los Alamos National Lab

JINA Online Seminar

Friday April 14$^{th}$ 2017

    LA-UR-16-27225

Motivation

The $r$ process is believed to be responsible for the production of roughly half the heavy elements on the periodic table.

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

This is a difficult problem

Couple together aspects of astrophysics with those of nuclear physics

On the astrophysics side

We classify environments by

Entropy or $S$

Timescale or $\tau$

Neutron-richness or $Y_e$

Ejected mass or $M_{ej}$

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

Inputs from nuclear physics

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

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

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

A Possible Path Forward

Complex problem - How can we approach a solution in the near term?

We can try to isolate the nuclear properties most important to measure which have an impact on both nuclear physics and astrophysics models

The reverse engineering framework is centered around the idea of providing feedback between these two components

A Typical $r$-process Calculation

nuclear physics + astrophysics ↦ abundances

Figure by A. Arcones (2011)

Reverse Engineering

What if we take a different approach?

Constrain nuclear physics with experiment and additionally observation using feedback from our calculated abundances

If we try to fit a particular part of the pattern we can ask what nuclear properties are responsible for its formation and learn how they are required to evolve with neutron excess

Reverse Engineering

Our pursuit must satisfy several constraints:

We must be able to make measurements on these nuclei

Limits us to nuclei closer to stability

So, we must explore the freeze-out phase of the $r$ process

We must be able to use a recognizable signature in the abundances

The rare earth peak

The Rare Earth Peak (REP)

This abundance feature is believed to be formed during freeze-out, when nuclei decay back to stability

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, $Y_e=0.3$

Kink in separation energies forms peak under hot freeze-out conditions

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

Formation of REP

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

Kink in neutron capture rates forms peak under cold freeze-out conditions

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)

REP Formation: Ideal Candidate

We choose to study method 1 for reverse engineering

  1. Dynamical formation during freeze-out ($R\lesssim1$)
    Requires a localized nuclear structure (kink)
    Relatively few nuclei to measure, close to stability
    Hints from Jin Wu's $T_{1/2}$ measurements
    Very close to making necessary mass measurements
  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

The Reverse Engineering Framework

The Bayesian Approach

An example... The Monty Hall problem

A new car is hidden behind one of the doors

The optimal strategy is to switch the initial pick - twice the chance of winning the new car

We update our probabilities based off new information

Apply Idea to REP Formation

For fixed astrophysical conditions (hot, cold or merger)...

Let's allow the nuclear masses to vary

We have to update all relevant nuclear physics self-consistently

The rare earth abundances provide feedback to the change in masses

Use the Metropolis algorithm to traverse the parameter space



Compute likelihood
$L\sim$ match red abundances
M. Mumpower et al. ApJ 833, 282 (2016)

Reverse Engineering Procedure

How it works in a nutshell

M. Mumpower et al. ApJ 833, 282 (2016)

Updating Nuclear Properties

Every time the masses change we recalculate...

Relevant Q-values

$\beta$-decay properties ($T_{1/2}$ and branching ratios)

Neutron capture rates

For hundreds of nuclei...

This is computationally expensive but necessary!

M. Mumpower et al. Phys. Rev. C 92 035807 (2015)

Updating Nuclear Properties

For $\beta$-decay we recalculate using the QRPA+HF model

Approximation: the $\beta$-strength remains unchanged

M. Mumpower et al. Phys. Rev. C 94 064317 (2016)

Results Of Reverse Engineering

First attempt

Hot wind $r$-process with default DZ parameters

Success?! ... We found a peak!But there's a problem!
$L\sim$ match red abundances

M. Mumpower et al. J. Phys. G 44 3 034003 (2017)

First attempt

Hot wind $r$-process with new DZ parameters

Success?! ... We found a peak! But there's a problem!
$L\sim$ match red abundances

M. Mumpower et al. J. Phys. G 44 3 034003 (2017)

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. J. Phys. G 44 3 034003 (2017)

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. J. Phys. G 44 3 034003 (2017)

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. ApJ 833, 282 (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 • tighter in N • larger change to masses

M. Mumpower et al. ApJ 833, 282 (2016)

Evolution of Abundances

Before • During • After peak formation

Great success!

Difference is encoded in the astrophysical conditions

M. Mumpower et al. ApJ 833, 282 (2016)

Predicted Masses

For three astrophysical evolutions: hot, cold or merger

The trend in the masses is important for forming the REP

M. Mumpower et al. J. Phys. G 44 3 034003 (2017)

Fit To Abundances

For three astrophysical evolutions: hot, cold or merger

M. Mumpower et al. J. Phys. G 44 3 034003 (2017)

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

Make the measurements to find out!

M. Mumpower et al. J. Phys. G 44 3 034003 (2017)

Algorithm Performance

Evolution of the fit to the REP versus Monte Carlo step

There are many ways we can upgrade the algorithm!

M. Mumpower et al. J. Phys. G 44 3 034003 (2017)

Where are we going?

Work by Nicole Vassh @ Notre Dame

Upgrades to the algorithm

Individual solar data uncertainties

Add in experimental data for network calculations

More robust description of fission

Explorations beyond the rare earth region...

Improving Our Network

PRISM: Portable Routines for Integrated nucleoSynthesis Modeling

Trevor Sprouse (Notre Dame)

Special thanks to

My collaborators

A. Aprahamian, M. Beard, D.-L. Fang, T. Kawano, G. C. McLaughlin, P. Möller, T. Sprouse, A. W. Steiner, N. Vassh & R. Surman

Summary

We have created a powerful framework for reverse engineering nuclear properties using $r$-process abundances.

The formation of rare earth peak is an ideal candidate for such a study because it is sensitive to nuclear physics inputs and astrophysical conditions.

We find distinct mass surface predictions for different astrophysical conditions.

These predictions will be testable in the lab within the next several years.

Future measurements and applications of this method will shed light on the formation of the rare earth peak and the astrophysical site of the $r$-process