Los Alamos National Lab

*JINA Online Seminar*

Friday April 14$^{th}$ 2017

LA-UR-16-27225

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

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 ($R$)

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

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

The chart of nuclides

All half-lives

Recently measured beta-decay half-lives

Recently measured beta-decay half-lives

Nuclear masses

Neutron capture rates

As of today, to varying degrees of accuracy

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

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

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*

nuclear physics + astrophysics ↦ abundances

Figure by A. Arcones (2011)

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

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

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

- Dynamical formation during freeze-out ($R\lesssim1$)

Requires a localized nuclear structure effect (kink) - Via fission fragment yields

Requires dumping heavy products in exactly the right spot

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)

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)

Using the ETFSI-Q mass model

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

Using the FRDM95 mass model

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

We choose to study method 1 for reverse engineering

- 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 - 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

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

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)

How it works in a nutshell

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

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)

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)

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)

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)

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)

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)

$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)

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)

Before • During • After peak formation

Great success!

Difference is encoded in the astrophysical conditions

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

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)

For three astrophysical evolutions: hot, cold or merger

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

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)

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)

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...

PRISM: Portable Routines for Integrated nucleoSynthesis Modeling

Trevor Sprouse (Notre Dame)

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

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*