Philip Mocz
NASA Einstein and Lyman Spitzer, Jr. Postdoctoral Fellow at Princeton University

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I am a NASA Einstein Fellow and Lyman Spitzer, Jr. Postdoctoral Fellow at Department of Astrophysical Sciences at Princeton University. I develop theory and high-performance simulations to study structure formation on scales from cosmology to star formation. I am at the forefront of research in fuzzy dark matter, which has seen considerable growing interest in the physics and astronomy communities over the last few years. The near-century-old dark matter problem is one of the most intriguing mysteries in modern physics: we do not know the nature of 84 percent of matter in the Universe, yet it is thought to govern cosmic structure and hold galaxies together. Ultralight (fuzzy) dark matter is a promising candidate, and I consider myself a leading expert in developing cosmological simulations of this type of dark matter fully coupled to baryonic physics. With these simulations, we can learn about the behavior of the theory and predict how future missions such as the James Webb Space Telescope could reveal the nature of the elusive dark matter particle. A second active research area of mine is the study of turbulent, self-gravitating systems. The theory of compressive turbulence lags behind the study of the incompressible Navier-Stokes equations. I work on developing it to gain physical insight into long-standing open problems, such as the inefficiency of star formation and the fundamental nature of turbulence.

I also develop a variety of new robust, high-performance methods for computational physics which I use in my every day work. My PhD thesis was completed at Harvard University with my advisor Lars Hernquist on moving mesh magnetohydrodynamics and applications to cosmology and star formation. As part of that work, I invented a new accurate method for solving the magnetohydrodynamic equations on a moving-mesh, which I implemented in the Arepo code. The method preserves mass, momentum, energy, the divergence-free property of the magnetic fields, and Galilean-invariance (exact advection).

I have broad interests in cosmology, galaxy evolution and feedback, black hole physics, structure formation, turbulence in the ISM, alternative theories of dark matter (fuzzy dark matter), numerical methods, computer visualization, and applications of machine learning and computer vision to astronomy.

I grew up in Hawaii and I love the outdoors.


Download my curriculum vitae (CV) [.pdf]


A complete record of my publications can be found using the searches below:

ADS search arXiv search Google scholar

Selected Recent Papers Subscribe to What's New

Galaxy Formation with BECDM - II. Cosmic Filaments and First Galaxies
Mocz, P.; Fialkov, A.; Vogelsberger, M.; Becerra, F.; Shen, X.; Robles, V.H.; Amin, M.A.; Zavala, J.; Boylan-Kolchin, M.; Bose, S.; Marinacci, F.; Chavanis, P.H.; Lancaster, K.; Hernquist, L.; 2019 MNRAS, submitted

First star-forming structures in fuzzy cosmic filaments
Mocz, P.; Fialkov A.; Vogelsberger, M.; Becerra, F.; Amin, M.A.; Bose, S.; Boylan-Kolchin, M.; Chavanis, P.H.; Hernquist, L.; Lancaster, L.; Marinacci, M.; Robles, V.H.; Zavala, J; 2019 Phys. Rev. Lett. (Editors' Selection) 123, 14

Fuzzy Dark Matter Soliton Cores around Supermassive Black Holes
Davies, E.Y.; Mocz, P.; 2019 MNRAS, 492, 5721

A Markov model for non-lognormal density distributions in compressive isothermal turbulence
Mocz, P.; Burkhart, B.; 2019 ApJL, 884, 2

Formation, Gravitational Clustering and Interactions of Non-relativistic Solitons in an Expanding Universe
Amin, M.; Mocz, P.; 2019 Phys. Rev. D, 100, 6

Heating of Milky Way disc stars by dark matter fluctuations in cold dark matter and fuzzy dark matter paradigms
Church, B.; Mocz, P.; Ostriker, J.P.; 2019 MNRAS, 485, 2861

Star formation from dense shocked regions in supersonic isothermal magnetoturbulence
Mocz, P.; Burkhart, B.; 2018 MNRAS, 480, 3916

On the Schrodinger-Poisson--Vlasov-Poisson correspondence
Mocz, P.; Lancaster, L.; Fialkov A.; Becerra, F.; Chavanis, P.H.; 2018 PhRvD, 97, 3519

Galaxy Formation with BECDM - I. Turbulence and relaxation of idealised haloes
Mocz, P.; Vogelsberger, M.; Robles, V.; Zavala J.; Boylan-Kolchin, M.; Fialkov A.; Hernquist, L.; 2017 MNRAS, 471, 4559

Moving mesh simulations of star forming cores in magneto-gravo-turbulence
Mocz, P.; Burkhart, B.; Hernquist, L.; McKee, C.; Springel, V.; 2017 ApJ, 838, 1


Selected highlights from my papers ...

How Dark Matter shapes First Galaxies

and how to tell if dark matter is fuzzy, warm, or cold

Turbulence Markov Model

to describe non-lognormal density distributions

Dynamical Friction

in fuzzy dark matter

Supersonic turbulence

dense structures in compressible turbulence

Solitons from early universe scalar fields

formation, gravitational clustering and interactions of solitons

Schrödinger to Vlasov

emergence of classical behavior from quantum mechanics

Axion Dark Matter

quantum turbulent properties

Star Formation

in magneto-gravo-turbulence

Primordial Magnetic Fields

in cosmological settings

Integer Lattice

for Vlasov-Poisson (6D)

Tidal Disruption Events


Moving Mesh Vector Potential CTA

for MHD

Quantum SPH

for the non-linear Schrödinger equations

Constrained Transport for MHD

on unstructured and moving meshes

Discontinuous Galerkin

on moving meshes


for 25,000 galaxies as function of environment

Supermassive Black Holes

cosmological growth and feedback

Inverse-Compton Ghosts

powerful double-lobed radio galaxies switched off

X-ray Winds

ionization structure of Seyfert 2 galaxy IRAS 18325-5926 with Chandra


Collaborators and students

(beta... Click button. It may take a few seconds to render. Interactive!)
connections in graph indicate co-authorships in papers I led

Mustafa A. Amin

Fernando Becerra

Katherine Blundell

Sownak Bose

Mike Boylan-Kolchin
UT Austin

Blakesley Burkhart

Pierre-Henri Chavanis

Pierre Christian
U. Arizona

Ben Church

Elliot Davies

Andy Fabian

Anastasia Fialkov

Shy Genel

Cara Giovanetti

Josep Miquel Girart

Karl Glazebrook

Alyssa Goodman

Andy Green

Lars Hernquist

Chat Hull

Yoni Kahn

Rahul Kannan

Shih-Ping Lai
Tsing Hua

Lachlan Lancaster

Julia Lee

Mariangela Lisanti

Avi Loeb

Max Malacari

Federico Marinacci

Chris McKee

Diego Munoz

Jerry Ostriker

Rudiger Pakmor

Victor Robles

Kevin Schaal

Xuejian Shen

Debora Sijacki

David Spergel

Volker Springel

Sauro Succi

Mark Vogelsberger

Jesus Zavala


List of courses at Harvard for which I have served as a Teaching Fellow:

  • Astronomy 151. Astronomical Fluid Dynamics. Spring 2016
  • Applied Computation 274. Computational Fluid Dynamics. Fall 2014
  • Applied Computation 274. Computational Fluid Dynamics. Spring 2014
  • Applied Mathematics 205. Advanced Scientific Computing: Numerical Methods. Fall 2012


List and links to selected outreach activities


Writings, software projects, interactive modules, tutorials, mini science investigations ...

  • Writings on Medium

    ~100 line Python tutorials for computational astro

  • April Fools Day arXiv Papers

    Check out the collection at

  • GPU Volume Rendering

    PAVOREAL (PArellel VOlume REndering ALgorithm) on GPUs

  • Interactive Mathematica Module on Shocks

    Explore the shock structure in the Euler and MHD Riemann problems

  • Cosmic-Ray Pressure MHD Instability

    Paper on my simulations of a cosmic-ray pressure gradient instability in a turbulent MHD environment at a shock interface, as part of my project for Astronomy 253 (plasma physics). Read the report (.pdf) and download the Matlab code

  • Bayesian Nested Sampling

    Bayesian nested sampling fitting of exoplanet radial velocity curve with 2 planets

  • SPH for Stellar Structure

    A simple introduction (.pdf) to smoothed-particle hydrodynamics (SPH), and writing your own code


Philip Mocz

Einstein Fellow


  • Department of Astrophysical Sciences
  • Princeton University
  • 4 Ivy Lane
  • Princeton, NJ 08544, USA
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