Sterile neutrinos as WDM and the 3.5 keV x-rayline

Alexey Boyarsky

Neutrino 2016. July 8

Evidence for Dark Matter

Stellar Disk

Dark Halo

Observed

Gas

M33 rotation curve

Expected: v(R) ∝ 1√R

Observed: v(R) ≈ const

Expected:masscluster =P

massgalaxies

Observed: 102 timesmore mass confiningionized gas

Lensing signal (directmass measurement)confirms otherobservations

Jeans instabilityturned tiny densityfluctuations into allvisible structures

Cosmological evidence for dark matter

I We see the structures in the Universe whenit was only 380 000 years old (encoded inthe anisotropies of the temperature of thecosmic microwave background)

I All the today’s structures are producedfrom tiny density fluctuations due togravitational Jeans instability

At CMB δρ/ρ ∼ 10−5, then grow δρ/ρ ∼ a (matter domination)atoday

adec= 1 + zdec ∼ 103 Not enough!

Some matter-like substance decoupled from photon gas should have beenpresent in the Universe at the time of decoupling

Is this neutrino Dark Matter?

I S. Tremaine and J. Gunn Phys. Rev. Lett. ( 1979)I The smaller is DM particle mass, the more particles is needed for a

given galaxy.I Fermions: phase-space number density should be smaller than that

of degenerate Fermi gas

⇒ If dark matter is made of fermions – its mass is bounded from below:

Mgal

4π

3R3

gal

14π

3v3∞

≤ 2mDM4

(2π~)3

I Objects with highest phase-space density – dwarf spheroidal galaxies– lead to the lower bound on the fermionic DM mass

mDM & 300− 400 eV

Neutrino dark matter

I However, if you compute contribution to DM density from massiveactive neutrinos (mν . MeV ), you get

Ων DMh2 =∑

mν

∫d3k

(2π)3

1

ekT + 1

=

∑mν [eV ]

94eV

I Using minimal mass of 300eV you get ΩDMh2 ∼ 3 (wrong byabout a factor of 30!)

I Sum of masses to have the correct abundance∑

mν ≈ 11eV

Massive Standard Model neutrinos cannot be simultaneously “as-trophysical” and “cosmological” dark matter: to account for themissing mass in galaxies and to contribute to the cosmological ex-pansion

Today this is confirmed by CMB, LSS and neutrino experimental data

Two generalizations of neutrino DM

Dark matter cannot be both light and weakly interacting at thesame time

Two classes of alternatives:

Light yet super-weakly inter-acting

I Can be light (down to

Tremaine-Gunn bound)

I Can be warm (born relativistic

and cool down later)

I Can be decaying (stability is not

required)

Heavy and therefore weaklyinteracting — WIMP

I shall not speak about it

Example: sterile neutrino dark matter

I For the early Universe, sterile neutrino is similar to the SM neutrino,but has en effective coupling constant ϑGF .

I Sterile neutrino is unstable (N → ννν)

I Subdominant (Br ∼ 1123 ) decay channel: N → ν + γ

νNs

e± ν

W∓

γW∓

ΓN→νγ =9αG 2

F

256π4ϑ2M5

N

Eγ =1

2MN

I Expect a signal from any large concentration of dark matter (galaxy,galaxy group, galaxy cluster)

Resonant enhancement

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.5

1.0

1.5

2.0

2.5

3.0

Momentum pM

EnergyE

HpLM

Resonant case

Shi & Fuller [astro-ph/9810076]

I In the presence of largelepton asymmetry theMSW resonance cantake place andproduction of sterileneutrinos becomes muchmore effective

10-5

10-4

10-3

10-2

0 1 2 3 4 5 6 7q

2 f

(q)

q = p/Tν

Non-resonantcomponent

Resonantcomponent

L6 = 16Ms = 3 keV

Laine & Shaposhnikov [0804.4543]

I The condition for resonance occursonly for specific values of momentum pand during limited period of time.

Warm dark matter (WDM)

I Particles are born relativistic⇒ they do not cluster

I Relativistic particles freestream out of overdenseregions and smooth primordialinhomogeneities

Overdensity

– Free-streaming scale:

λcoFS =

∫ t

0

v(t ′)dt ′

a(t ′)= 1 Mpc

(keV

Msterile

)

Particle velocities means that warm dark matter has effective pres-sure that prevents small structure from collapsing

Suppression of power spectrumUniversity of Durham

Institute for Computational Cosmology

The dark matter power spectrum

Free streaming à

 λcut α mx-1

for thermal relic

 mCDM ~ 100GeV susy; Mcut ~ 10-6 Mo

mWDM ~ few keV sterile ν; Mcut~109 Mo

 mHDM ~ few eV light ν; Mcut~1015 Mo

The linear power spectrum (“power per octave” )

warm

cold

Dwarf gals

galaxy clusters

hot

k3 P(k) HDM

Large scales small scales

Fluc

tuat

ion

ampl

itude

Log k [h Mpc-1]

Log

k3P

(k)

1

k3P(k) ∼ |δk |2

Halo substructure in ”cold” DM universe

COLD DM models predict millions of sub-

structures within a galaxy like Milky Way

Only ∼ 30 are observed within our Galaxy.

M. Geha 2010Is small number of observed substructures due to dark matterfree-streaming? Moore et al. (1999), Klypin et al. (1999) and 1000s of others

Halo substructure in ”warm” DM universe

Simulated HNL dark matter halo is compatible with the Lyman-αforest data but provides a structure of Milky way-size halo differentfrom CDM

Lyman-α forest and power spectrum

Lyman-α forest data

0 1000 2000 3000 4000 5000vel (km/s)

0.0

0.2

0.4

0.6

0.8

1.0

flu

x

ΛCDMWDM 2 keVWDM 1 keV

10-4

10-3

10-2

10-1

100

101

102

103

104

10-4 10-3 10-2 10-1 100 101

P(k

) [(

Mp

c/h

)3 ]

k [h/Mpc]

CDM

WDM ⇒

0.001 0.010 0.100 k (s/km)

0.01

0.10

1.00

∆2

F(k

)z=2.2

z=2.4

z=2.6

z=2.8

z=3

z=3.2

z=3.4z=3.6z=3.8

z=4.0

z=4.2

z=4.6

z=5

z=5.4

cosmic time: 1.1-3.1 Gyr

cosmic scales: 0.5/h-50/h com. Mpc

SDSS

MIKE&HIRES

best fit ΛCDM

WDM 2.5 keV

Warm dark matter predicts suppression (cut-off) in the flux powerspectrum derived from the Lyman-α forest data

Suppression in the flux power spectrum

0.001 0.010 0.100 k (s/km)

0.01

0.10

1.00

∆2F(k

)

z=2.2

z=2.4

z=2.6

z=2.8

z=3

z=3.2

z=3.4z=3.6z=3.8

z=4.0

z=4.2

z=4.6

z=5

z=5.4

cosmic time: 1.1-3.1 Gyr

cosmic scales: 0.5/h-50/h com. Mpc

SDSS

MIKE&HIRES

best fit ΛCDM

WDM 2.5 keV

Suppression in the flux powerspectrum may be due to

I Pressure (Jeansbroadening) – preventsclustering

I Temperature (Doppler

broadening√

2kTmp

) –

increases hydrogenabsorption line width

I Warm dark matter

Warm dark matter + cold IGM

3.5 4.0 4.5 5.0 5.5 6.0 6.5z

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6 T

0/[

10

4 K

]

power-law ev.

z-binned ev.

Becker+11 (γ=1.0)

Becker+11 (γ=1.3)

Becker+11 (γ∼1.5)

Bolton+12

7500 10000 12500

T0[K](z = 4.2)

0.00

0.15

0.30

0.45

0.60

1/(m

WD

M[k

eV

])

7500 10000 12500

T0[K](z = 4.6)

0.00

0.15

0.30

0.45

0.60

1/(m

WD

M[k

eV

])

2500 5000 7500

T0[K](z = 5.0)

0.00

0.15

0.30

0.45

0.60

1/(m

WD

M[k

eV

])

5000 10000 15000 20000

T0[K](z = 5.4)

0.00

0.15

0.30

0.45

0.60

1/(m

WD

M[k

eV

])

daw

Data prefers cold IGM medium around redshift z = 5 ⇒ powerspectrum suppression is due to something else?

A. Garzilli, A. Boyarsky, O. Ruchayskiy [1510.07006]

Alternative way to measure temperature

Antonella Garzilli - Leiden University

r2kBT

mH

H(z)F

IGM temperature from line broadening

Garzilli, Theuns, Schaye MNRAS 450, 2 (2015)

Decaying dark matter

Decaying dark matter?

I Two-body decay into two massless particles (DM→ γ + γ or

DM→ γ + ν) ⇒ narrow decay line

Eγ =1

2mDMc2

I The width of the decay line is determined by Doppler broadeningI Typical virial velocities:

I A dwarf satellite galaxy: ∼ 30 km/secI Milky Way or Andromeda-like galaxy: ∼ 200 km/secI Typical velocity in the galaxy cluster ∼ 1500 km/sec

I Very characteristic signal: narrow line in all DM-dominated objects

with∆E

Eγ∼ vvir

c∼ 10−4 ÷ 10−2

Search for decaying dark matter

DM decay signal from a galaxy DM annihilation signal from a galaxy

Restrictions on life-time of decaying DMSee A White Paper on keV Sterile Neutrino Dark Matter [1602.04816]

Life

-tim

e τ

[sec

]

MDM [keV]

1025

1026

1027

1028

1029

10-1 100 101 102 103 104

XMM, HEAO-1 SPI

τ = Universe life-time x 108

Chandra

PSD

exc

eeds

deg

ener

ate

Fer

mi g

as

0.01 0.1 1 10 102

103

104

1026

1027

1028

mΦ @MeVDΤ

@sec

D

Φ®ΓΓ

HEAO-1

INTEGRAL

COMPTEL

EGRET

FERMI

3.5 keV line.Two groups reported an identified feature in the X-ray spectra of dark matter-dominated objets

ApJ (2014) [1402.2301]

PRL (2014) [1402.4119]

I Energy: 3.5 keV. Statistical error for line position ∼ 30− 50 eV.

I Lifetime: ∼ 1028 sec (uncertainty: factor ∼ 3)

I Possible origin: decay DM→ γ + ν (fermion) or DM→ γ + γ (boson)

Subsequent worksFor overview see e.g. [1602.04816] “A White Paper on keV Sterile Neutrino Dark Matter”

I Subsequent works confirmed the presenceof the 3.5 keV line in some of the objectsBoyarsky et al., Iakubovskyi et al.; Franse et al.;

Bulbul et al.; Urban et al.; Jeltema & Profumo

I challenged it existence in other objectsMalyshev et al.; Anderson et al.; Tamura et al.;

Sekiya et al.

I argued astrophysical origin of the lineGu et al.; Carlson et al.; Jeltema & Profumo;

Riemer-Sørensen; Phillips et al.

A common explanation for every detectionand non-detection?

I When comparing bounds from different objects one should be careful –

uncertainty in the dark matter content in each of them results in large

Dark matter is universal

Dark matter is a universal substance, present in everygalaxy (spiral, elliptical, dwarf spheroidal) and everygalaxy clusterFrom the point of view of astrophysical processes these objects are verydistinct!

Analysis of Draco dSph[1512.07217]

I The line is detected in thespectrum of Draco dSph withlow (2σ) significance

I Line flux/position are consistentwith previous observations

I There is a shift in position(∼ 1σ) between twoXMM-Newton detectors (which

happens for weak lines)

I The data is consistent with DMinterpretation for lifetimeτ > (7−9)× 1027 sec

I Compared to [1512.01239] we do

data processing differently and use a

more sophisticated background

model.

Flux [cts/sec/cm2]

Line position [keV]

0.0x100

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

2.5x10-6

3.0x10-6

3.5x10-6

4.0x10-6

4.5x10-6

3.48 3.5 3.52 3.54 3.56 3.58 3.6

M31

GC

Distant clusters (MOS)

Distant clusters(PN)

All clusters(MOS)

Best-fit Draco PN

PN camera flux [cts/sec/cm2]

Line position [keV]

∆χ2 = 1

∆χ2 = 4

∆χ2 = 9

0.0x100

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

2.5x10-6

3.0x10-6

3.5x10-6

3.46 3.48 3.5 3.52 3.54 3.56 3.58 3.6 3.62 3.64

M31

GC

Distant clusters

Distant clusters(PN)

All clusters(MOS)

Best-fit Draco MOS1+MOS2+PN

Next step for 3.5 keV line: Astro-H

I Astro-H – new generation X-rayspectrometer with a superb spectralresolution

I Launched 17 February 2016

I Calibration phase – about 1 year

I First observational/calibration target –Perseus galaxy cluster, where strong3.5 keV line has been detected

I Expected to be able to confirm thepresence of the 3.5 keV line in Perseusand distinguish it from atomic elementlines (Potassium, Chlorium, etc.)

0

1

2

3

4

5

6

7

8

9

10

400 450 500 550 600 650 700

Cou

nt r

ate,

arb

. uni

ts

Energy [eV]

XMM spectrumResolved spectrum

3 3.2 3.4 3.6 3.85×10

−410

−31.

5×10

−3

Flux

(ph

cm-2s

-1keV

-1)

Energy (keV)

Astro-H SXSPerseus, 1 MseckT = 6.5 keV, 0.6 solarz=0.0178v(baryons) = 300 km/sv(line) = 1300 km/s

3.55 keV Line

Ar XVII

Ar XVIII

Ca XIX3.62 keVAr XVII DR

HOWEVER

Status of Astro-H/Hitomi4.1 PresumedMechanism(Summary)(From“Normalsituation”tothe“AttitudeanomalyEvent”,and“Objectsseparation”)

29(*)Unloading䠖Operation to decrease the momentum kept in RW within the range of designed range.

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䠄䠐䠅㻶㼡㼐㼓㼕㼚㼓 㼠㼔㼑 㼟㼍㼠㼑㼘㼘㼕㼠㼑 㼕㼟 㼕㼚 㼠㼔㼑 㼏㼞㼕㼠㼕㼏㼍㼘 㼟㼕㼠㼡㼍㼠㼕㼛㼚㻘 㻭㻯㻿 㼟㼣㼕㼠㼏㼔㼑㼐 㼠㼛 㻿㼍㼒㼑 㻴㼛㼘㼐 㼙㼛㼐㼑 㻔㻿㻴㻕㻘 㼍㼚㼐 㼠㼔㼑㼠㼔㼞㼡㼟㼠㼑㼞㼟 㼣㼑㼞㼑 㼡㼟㼑㼐㻚 㻭㼠 㼠㼔㼕㼟 㼠㼕㼙㼑 㻭㻯㻿 㼜㼞㼛㼢㼕㼐㼑㼐 㼍㼠㼥㼜㼕㼏㼍㼘 㼏㼛㼙㼙㼍㼚㼐 㼠㼛 㼠㼔㼑 㼠㼔㼞㼡㼟㼠㼑㼞㼟 㼎㼥 㼠㼔㼑㼕㼚㼍㼜㼜㼞㼛㼜㼞㼕㼍㼠㼑 㼠㼔㼞㼡㼟㼠㼑㼞 㼏㼛㼚㼠㼞㼛㼘 㼜㼍㼞㼍㼙㼑㼠㼑㼞㼟㻚 㻭㼟 㼍 㼞㼑㼟㼡㼘㼠㻘 㼕㼠 㼠㼔㼞㼡㼟㼠㼑㼐 㼕㼚 㼍㼚 㼡㼚㼑㼤㼜㼑㼏㼠㼑㼐 㼙㼍㼚㼚㼑㼞㻘 㼍㼚㼐 㼕㼠 㼕㼟㼑㼟㼠㼕㼙㼍㼠㼑㼐 㼠㼔㼍㼠 㼠㼔㼑 㼟㼍㼠㼑㼘㼘㼕㼠㼑 㼞㼛㼠㼍㼠㼕㼛㼚 㼣㼍㼟 㼍㼏㼏㼑㼘㼑㼞㼍㼠㼑㼐㻚 䛆 㻼㼞㼑㼟㼡㼙㼑㼐 㻹㼑㼏㼔㼍㼚㼕㼟㼙 㻟䛇

凚凧凛㻿㼕㼚㼏㼑 㼠㼔㼑 㼞㼛㼠㼍㼠㼕㼛㼚 㼟㼜㼑㼑㼐 㼛㼒 㼠㼔㼑 㼟㼍㼠㼑㼘㼘㼕㼠㼑 㼑㼤㼏㼑㼑㼐㼑㼐 㼠㼔㼑 㼐㼑㼟㼕㼓㼚㼑㼐 㼟㼜㼑㼑㼐㻘 㼜㼍㼞㼠㼟 㼛㼒 㼠㼔㼑 㼟㼍㼠㼑㼘㼘㼕㼠㼑 㼠㼔㼍㼠 㼍㼞㼑㼢㼡㼘㼚㼑㼞㼍㼎㼘㼑 㼠㼛 㼠㼔㼑 㼞㼛㼠㼍㼠㼕㼛㼚 㼟㼡㼏㼔 㼍㼟 㼟㼛㼘㼍㼞 㼍㼞㼞㼍㼥 㼜㼍㼐㼐㼘㼑㼟 㻔㻿㻭㻼㼟㻕㻘 㻱㼤㼠㼑㼚㼟㼕㼎㼘㼑 㻻㼜㼠㼕㼏㼍㼘 㻮㼑㼚㼏㼔 㻔㻱㻻㻮㻕 㼍㼚㼐㼛㼠㼔㼑㼞㼟 㼟㼑㼜㼍㼞㼍㼠㼑㼐 㼛㼒㼒 㼒㼞㼛㼙 㼠㼔㼑 㼟㼍㼠㼑㼘㼘㼕㼠㼑㻚 㼀㼔㼑㼞㼑 㼕㼟 㼔㼕㼓㼔 㼜㼛㼟㼟㼕㼎㼕㼘㼕㼠㼥 㼠㼔㼍㼠 㼠㼔㼑 㼎㼛㼠㼔 㻿㻭㻼㼟 㼔㼍㼐 㼎㼞㼛㼗㼑㼚 㼛㼒㼒 㼍㼠㼠㼔㼑㼕㼞 㼎㼍㼟㼑㼟 㼍㼚㼐 㼣㼑㼞㼑 㼟㼑㼜㼍㼞㼍㼠㼑㼐㻚 傜 㻼㼞㼑㼟㼡㼙㼑㼐 㻹㼑㼏㼔㼍㼚㼕㼟㼙 㻠傝

Considering the information above, JAXA concluded that the satellitesfunctionality could not be restored and ceased recovery activities. (April28)

Before its failure Astro-H/Hitomi had started itsobservational programme

I There are observations of the center of Perseus galaxy clusterFirst results appeared two days ago in Nature Letters

Astro-H vs. Suzaku spectrum. Nature (2016)

3.5 keV line with Astro-H/Hitomi

I The center of Perseus galaxy cluster exhibits one of the strongestsignals at 3.5 keV with the flux F ∼ 2× 10−5 cts/sec/cm2

(confirmed by several groups and observed with 3 instruments)

I Exposure of the published data – 230 ksec

I The data at energies below 5.5 keV has not been revealed by thecollaboration

I It is difficult to make any estimates because the calibration phase “. . . includes a beryllium window that absorbs most X-rays belowabout 3keV”

I We hope that it will be possible to confirm the presence of the3.5 keV line in Perseus and distinguish it from atomic element lines(Potassium, Chlorium, etc.)

Future

Microcalorimeter on sounding rocket (2017)

I Instrument with largefield-of-view and very highspectral resolution

I Very useful to resolve narrowlines from diffuse sources

I Fly time ∼ 102 seconds pointingto some area in the sky ⇒ canonly explore a signal fromGalactic dark matter halo

[keV]S

m1 10

θ2

2sin

12−10

11−10

10−10

9−10

8−10

7−10

6−10

5−10

4−10

(1)

(2,3)

6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.511−10

10−10

9−10

(1)

(2,3)

Athena+

I Large ESA X-ray mission (2028)

I X-ray spectrometer (X-IFU) – unprecedented spectralresolution

I Lifetime: 5–10 years

I Very large collecting area (10× that of XMM)

Thank you for your attention

Draco dSph 2015 observations[1512.07217]

2 3 4 5 6 7 8 9 10

0.1

0.05

0.2

norm

aliz

ed c

ount

s s−

1 ke

V−

1

Energy (keV)

Draco spectra binned by 65 eV, mos1 (black), mos2 (red), pn (green)

Raw/Cleaned FoV[Msec] [arcmin2]

MOS1 1.43 / 0.97 318.9MOS2 1.44 / 1.02 573.5PN 1.29 / 0.65 543.9

0

0.1

0.2

norm

aliz

ed c

ount

s s−

1 ke

V−

1

PN 65 eV

3 3.5 4 4.5 5 5.5 6 6.5

−5×10−3

0

5×10−3

norm

aliz

ed c

ount

s s−

1 ke

V−

1

Energy (keV)

Draco dSph in 2009 vs. 2015

2 4 6 8 10

0.1

0.0

5

no

rma

lize

d c

ou

nts

s−

1 k

eV

−1

Energy (keV)

Draco MOS spectra binned by 65 eV, 2009 year (black), 2015 year (red)

2 4 6 8 10

10

.20

.52

no

rma

lize

d c

ou

nts

s−

1 k

eV

−1

Energy (keV)

Draco PN spectra binned by 65 eV, 2009 year (black), 2015 year (red)

Jeltema & Profumo (2015)- I

I Independent analysis of the 2009+2015 Draco observations wasdone in [1512.01239]

I No line detected even in PN camera

I Much stronger upper limits on flux

Black cross: detection of Ruchayskiy et al.[1512.07217]

Black down arrow: 2σ upper limit fromRuchayskiy et al. [1512.07217]

I JP15 [1512.07217] is a very succinct paper. No details of dataanalysis. Trying to reproduce the results we made a number ofmodifications of our procedure

Jeltema & Profumo (2015)- II

PN dataset/data processing Flux, 10−6 ph/cm2/s ∆χ2

2015 year dataset (26 obs.) used in R15

65 eV bin, 2.3-11 keV, NXB+CXB 1.65+0.67−0.70 5.3

65 eV bin, 2.3-11 keV, NXB+CXB no OOTcorr.

1.57+0.74−0.74 4.3

5 eV bin, 2.3-11 keV, NXB+CXB 1.50+0.67−0.71 4.4

5 eV bin, 2.5-5 keV, NXB+CXB 1.56+0.71−0.76 3.9

5 eV bin, 2.5-5 keV, NXB 1.18+0.71−0.70 2.8

2009+2015 years dataset (31 obs.) used in JP15

65 eV bin, 2.3-11 keV, NXB+CXB 1.47+0.72−0.74 4.2

5 eV bin, 2.5-5 keV, NXB 1.04+0.66−0.70 2.2