The Thermal and Gravitational Energy Densities in the Large- scale Structure of the Universe

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Eiichiro Komatsu, The MPA Institute Seminar, March 1, 2021

The Thermal and Gravitational Energy Densities in the Large-

scale Structure of the Universe

Cr edit: Dylan Nelson, Illustris Collaboration

Chiang, Makiya, Ménard, EK (2020)

Chiang Makiya Ménard

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Outline

Three questions to answer (hopefully) during this talk

1. How hot is the large-scale structure of the Universe today? How was it before?

•

Chiang, Makiya, Ménard, EK, ApJ, 902, 56 (2020) 2. Where did the thermal energy come from?

•

Chiang, Makiya, EK, Ménard, ApJ, in press (arXiv:2007.01679) 3. What is our result good for?

•

Is it just a nice measurement with a nice interpretation, or actually useful for something? (Young, EK, Dolag, in preparation)

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MP A Pr ess Release, November 10, 2020

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JHU Pr ess Release, November 10, 2020

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The cosmic energy inventory

Fukugita & Peebles (2004)

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We know the mean total mass density of the Universe: Ωm ~ 0.3.

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We also know the mean baryonic mass density of the Universe: ΩB ~ 0.05.

•

We also have estimates for many other energy densities in the Universe:

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Fukugita & Peebles (2004)

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Fukugita & Peebles (2004)

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But we did not know the mean thermal energy density of the Universe, Ωth

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Let’s measure this! ⁷

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Our definition of the thermal energy density

nk

B

T rather than (3/2)nk

B

T

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We define the thermal energy from kBT, rather than the kinetic energy, (3/2)kBT.

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If you do not like this definition, keep this factor of 3/2 in your mind.

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Then the mean (comoving) thermal energy density is equal to the mean thermal pressure in the comoving volume:

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Order-of-magnitude estimate

There is more than one way to do this. Here is one example.

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^P^th^{= ρ}^gas^σ²^{, where σ}² is some typical 1D velocity dispersion in the large-scale structure.

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^Ω^th^{= Ω}^gas^σ²^{~ 2x10}^–8^(Ω^gas/0.05)(σ/200 km/s)²

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Spoiler: our measurement gives Ωth = (1.7±0.1)x10^–8 at z=0. Not bad, but this isn’t actually the right way to do it in detail.

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OK, let’s go. We use the thermal Sunyaev-Zeldovich eﬀect to do this measurement.

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Mroczkowski et al. (2019)

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Mroczkowski et al. (2019)

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Mroczkowski et al. (2019)

Reduced intensity at low frequencies

Enhanced intensity

at high frequencies

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Mroczkowski et al. (2019)

Reduced intensity at low frequencies

Enhanced intensity

at high frequencies

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Mroczkowski et al. (2019)

Reduced intensity at low frequencies

Enhanced intensity

at high frequencies

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Where is a galaxy cluster?

Subaru image of RXJ1347-1145 (Medezinski et al. 2010) http://wise-obs.tau.ac.il/~elinor/clusters

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Where is a galaxy cluster?

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Visible

Ground-based

Telescope (Subaru)

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Hubble image of RXJ1347-1145 (Bradac et al. 2008)

Visible

Hubble Space

Telescope

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Chandra X-ray image of RXJ1347-1145 (Johnson et al. 2012)

X-ray

Chandra

Space Telescope

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Chandra X-ray image of RXJ1347-1145 (Johnson et al. 2012)

ALMA Band-3 Image of the

Sunyaev-Zel’dovich effect at 92 GHz (Kitayama et al. 2016)

Microwave!

Atacama Millimeter and Submillimeter Array (ALMA)

1σ=17 μJy/beam

=120 μK

CMB

5” resolution

(World record)

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Multi-wavelength Data

Optical:

•10

^2–3

galaxies

•velocity dispersion

•gravitational lensing

X-ray:

•hot gas (10

^7–8

K)

•spectroscopic T

X

•Intensity ~ n

e2

L

I_X =

Z

dl n²_e⇤(T_X )

SZ [microwave]:

•hot gas (10

^7-8

K)

•electron pressure

•Intensity ~ n

e

T

e

L

I_SZ = g_⌫ ^T k_B m_ec²

Z

dl n_eT_e

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SZ X-ray

They are similar, but not quite the same

This is the first time to compare SZ and X-ray images at a comparable angular resolution.

Electron Pressure View Density View

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SZ X-ray

Let’s subtract a smooth component

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Let’s subtract a smooth component

SZ X-ray

Electron Pressure View Density View

Ueda et al. (2018)

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Another example: Phoenix Cluster (z=0.597)

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SZ X-ray

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Kitayama et al. (2020)

Electron Pressure View Density View

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Another example: Phoenix Cluster (z=0.597)

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SZ X-ray

Electron Pressure View Density View

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Kitayama et al. (2020)

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Q1: How hot is the large-scale structure of the Universe?

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Create a full-sky SZ map using the multi-frequency data!

Chiang, Makiya, Ménard, EK, ApJ, 902, 56 (2020)

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Full-sky Electron Pressure Map

North Galactic Pole South Galactic Pole

Planck Collaboration

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The Limitation of the SZ data

The need for “Tomography”

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This map gives us all the hot electron pressure in projection.

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No redshift information.

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We can overcome this limitation by cross-correlating the SZ map with the locations of galaxies with the known redshifts => the SZ tomography.

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1

2 3 4

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h

^SZ

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_SZ

(2) i

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h ^SZ(1) _gal(4)i

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h ^SZ(2) _gal(3)i

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h ^gal(3) _gal(4)i

Makiya, Ando & EK (2018)

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The data used

Planck and SDSS

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For the SZ: Multi-frequency component separation

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The Planck High-frequency Instrument (HFI) data at 100, 143, 217, 353, 545 and 857 GHz.

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In addition, we use the IRAS data at 3 and 5 THz for better separating the cosmic infrared background (CIB; from dusty galaxies).

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For the galaxies and quasars: 2 million redshifts at 0<z<3

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The SDSS main, SDSS-III/BOSS, and SDSS-IV/eBOSS data sets.

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http://tomographer.org

See Chiang’s versatile cross-correlation tool, “Tomographer”:

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We focus on the clustering signal at large scales (the so-called “2-halo term” of clustering).

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Ignore non-linear clustering inside dark matter halos, but focus only on clustering between distinct halos.

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In this limit, we can write Pe = <Pe>(1+byδmatter) and ngal = <ngal>(1+bgalδmatter).

Thus, the cross-correlation yields

The basic methodology: A heuristic description

Vikram, Lids & Jain (2017)

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What we measure from the cross-correlation

The first key deliverable

What we want in the end

Measured from the auto galaxy correlation From the ΛCDM model

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h P _e n _gal i

b _gal h n _gal ih matter matter i = b _y h P _e i

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How the measurements look

To show that we are in the “linear” regime

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The data within the grey band are used for the analysis, where the ratio is a

constant, justifying the extraction of the single constant amplitude in each z bin.

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h I

SZ

n

gal

i h n

gal

ih

mattermatter

i

Chiang et al. (2020)

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The SZ signal (decrement)!

The CIB

The Planck/IRAS-SDSS cr oss-corr elations The need for the multi-component fits (SZ+CIB).

Chiang et al. (2020)

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Tomography of the SED of not only SZ, but also CIB!

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Chiang et al. (2020)

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The first main result: Model-independent

Bias-weighted mean electron pressure of the Universe!

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Chiang et al. (2020)

The first measurements using spectroscopic

redshifts; thus, our binned data points are independent.

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<bP e > -> <P e >

Debiasing by the physical model

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To get the mean pressure, we need to “de-bias” <bPe> = by<Pe>. This can be done by computing and dividing by

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b _y (z ) = h bP _e i

h P _e i =

R dM _dM ^dn M ^5/3+↵

^P

b _halo (M, z ) R dM _dM ^dn M ^5/3+↵

^P

αP = 0.12 is the empirical correction for

non-self-similar scaling found by the X-ray data (Arnaud et al. 2010).

Excellent agreement with the measurement from the Magneticum Simulation (Young, EK, Dolag, in prep)

Chiang et al. (2020)

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The second main result

The mean thermal energy density of the Universe!

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Density-weighted mean temperatur e of the Universe

Chiang et al. (2020)

2 million K today; the 3-fold

increase over the last 8 billion years

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The prediction for the future space mission

The sky-averaged Compton y parameter

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Chiang et al. (2020)

•

Sometime in future, there will be a space mission

measuring the sky-

averaged (monopole) spectrum of the CMB, improving upon COBE/

FIRAS by a factor of 10^3–5.

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Such a mission will measure the average distortion from the hot gas in the Universe.

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Our data suggest

<y>=1.2x10

^–6

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Q2: Where did the thermal energy come from?

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Chiang, Makiya, EK, Ménard (2021), arXiv:2007.01679

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Of course you know the answer…

Open any textbook!

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You can find a statement like, “As the large-scale structure forms and the

matter density fluctuation collapses, the gravitational energy is converted into the thermal energy via a shock.”

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Yes, of course this picture is correct. However, how much do we know about this energy conversion quantitatively?

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To my knowledge, no quantitative assessment of this statement has been made before.

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Our approach: We have measured Ωth. We can calculate Ωgrav using theory of the structure formation. Let’s compare the two and see if they make sense.

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The ensemble average is given by the density-potential cross power spectrum:

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Section 9 of Peebles’s Book in 1980

The “W”: Gravitational potential energy per unit mass

With the Poisson equation:

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Section 9 of Peebles’s Book in 1980

The “W”: Gravitational potential energy per unit mass

This is the exact formula for W (in the Newtonian limit).

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The Energy Balance in the Large-scale Structure

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Chiang et al. (2021), arXiv:2007.01679

The energy density parameter for W:

The halo contribution:

Pressure available for baryons

The total gravitational ener

gy density The gravitational ener

gy density in halos

The kinetic ener

gy available for baryonic pr

essure

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Conclusion from the second part

The energy balance does work, but where is the rest of the K.E.?

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We can now make the following statement:

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The measured thermal energy density accounts for ~80% of the

gravitational potential energy available for kinetic energy of collapsed baryons.

•

This is the first quantitative assessment of the textbook statement on gravitational -> thermal energy conversion in the large-scale structure formation (using the observational data).

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What is the rest (~20%)? => Non-thermal pressure due to the mass accretion!

[Shi and EK (2014); Shi et al. (2015; 2016)]

•

There is a lot more (x3) kinetic energy available in the LSS beyond collapsed baryons. Where/how can we find it? Kinetic SZ eﬀect?

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Q3: Is this good for anything?

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Is this just beautiful physics, or actually useful for anyone?

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“Thermometer” test of your hydro simulation

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Measurement fr

om the Magneticum Simulation (Sam Young)

Young, EK, Dolag, in preparation

↓

↓ ↓ ↓

Chiang et al

ΔT Δb_y

Halo model

0.0 0.5 1.0 1.5 2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Redshift z

AverageTemperatureT(MK)

•

How hot is your hydro simulation?

•

All you need is the average temperature: Super easy to compute.

•

It is possible that all of the current generation of hydro simulations pass this test; in that case this test is too easy to be useful :)

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Conclusions

The energy balance seems to work in the Universe

•

We have measured the evolution of the mean thermal energy density

(equivalently the density-weighted mean temperature) of the large-scale structure of the Universe out to z~1.

•

Personally: This is the completion of the 20 years of homework since Refregier, EK, Spergel, Pen (2000). We used Ue-Li Pen’s moving mesh hydro code to predict the evolution of the density-weighted mean

temperature. We finally measured this.

•

Detailed comparison to the gravitational energy of the LSS shows that the

thermal energy accounts for ~80% of the kinetic energy available for thermal pressure of collapsed baryons. The rest can be accounted for easily by non- thermal pressure (Shi & EK 2014).

•

Is this good for anything? You tell us!

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W to K: the mean kinetic energy per unit mass

Layzer-Irvine equation (Layzer 1963; Irvine 1961; Dmitriev & Zeldovich 1964)

•

Given the knowledge of W, we can calculate the mean kinetic energy per unit mass, K, using the Layzer-Irvine equation:

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•

The initial condition for K can be set using the linear theory result at suﬃciently early time (Davis et al. 1997),

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W to K: The Result

More kinetic energy is available than the virial theorem K = –W/2

•

This result captures the kinetic energy of all structures.

•

Here, we do not separate

random and bulk motion of

collapsed and non-collapsed structures, respectively.

•

For comparison to the thermal energy, we used the virial

relationship, K = –W/2.

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