sterile neutrinos as subdominant warm dark matter

Sterile Neutrinos As Subdominant Warm Dark

Matter

Sterile Neutrinos As Subdominant Warm Dark

Matter

D.T. CumberbatchOxford University, Astrophysics

Dept.

D.T. CumberbatchOxford University, Astrophysics

Dept. A. Palazzo, D. Cumberbatch, A. Slosar and J. Silk (arXiv:0707.1495)

OutlineOutline Introduction

Neutrinos and the dark sector Sterile neutrino properties Motivations for keV sterile neutrino dark matter (SN DM)

Current experimental constraints on dominant SN DM X-rays Lyman-

Experimental constraints on sub-dominant SN DM HEAO-1 (diffuse X-ray background) SDSS (Ly-)

Theoretical predictions vs. Experimental constraints Qualitative/Quantitative treatments of hadronic uncertainties Determination of upper limits on fs

Summary & Conclusions

Introduction Neutrinos and the dark sector Sterile neutrino properties Motivations for keV sterile neutrino dark matter (SN DM)

Current experimental constraints on dominant SN DM X-rays Lyman-

Experimental constraints on sub-dominant SN DM HEAO-1 (diffuse X-ray background) SDSS (Ly-)

Theoretical predictions vs. Experimental constraints Qualitative/Quantitative treatments of hadronic uncertainties Determination of upper limits on fs

Summary & Conclusions

Motivation for DMMotivation for DMRotation Curves of spiral galaxies:

Abell 1689, HST

Galaxy clusters:• Proper motion

• X-ray emissions from hot gas• Gravitational lensing

Large-scale structure

• M/L ratio

2dFGRS

WMAP

Anisotropies in the CMB

Neutrinos and the dark sector

Neutrinos and the dark sector

There are many particle candidates for dark matter (e.g. sparticles, axions, etc.), but the only observed candidate is the weakly-interacting (left-handed) neutrino (m~eV).

However, measurements of large-scale structure and the power spectrum of CMB anisotropies imply h2<0.0067 (95% C.L.)

Particle theory also allows for the existence of a right-handed “sterile neutrino”, which many have proposed could be a viable dark matter candidate.

There are many particle candidates for dark matter (e.g. sparticles, axions, etc.), but the only observed candidate is the weakly-interacting (left-handed) neutrino (m~eV).

However, measurements of large-scale structure and the power spectrum of CMB anisotropies imply h2<0.0067 (95% C.L.)

Particle theory also allows for the existence of a right-handed “sterile neutrino”, which many have proposed could be a viable dark matter candidate.

What are Sterile Neutrinos?What are Sterile Neutrinos?

Electroweak singlet (Bruno Pontecorvo, (1967) ) No weak interactions (i.e. “sterile” or right-handed) Natural explanation for small (but finite) “active”

neutrino masses Introduced through the seesaw Lagrangian (Minkowski)

Electroweak singlet (Bruno Pontecorvo, (1967) ) No weak interactions (i.e. “sterile” or right-handed) Natural explanation for small (but finite) “active”

neutrino masses Introduced through the seesaw Lagrangian (Minkowski)

Variety of production mechanismsNon-resonant oscillationsResonant oscillations

€

L = LSM + v s,a (iγ μ∂μ )vs,a − yαaHl α vs,a −Maα

2v s,a

c vs,a + h.c.

Ma»100GeV or as small as ~eVFor Ma ~ EEW and ya, MSM provides correct a massesMasses of lightest neutrinos suppressed by <H>/ Ma

Non-resonant OscillationsNon-resonant Oscillations Produced through a-s oscillations involving off-

diagonal elements of mixing matrix (hence no coupling to SM Gauge bosons)

Don’t require finite lepton asymmetry Simplest model: Dodelson-Widrow (DW) mechanism

Standard thermal history No additional couplings required Produces minimal relic density

Alternatives to DW Entropy dilution (Abazajian & Fuller, Abazajian &

Koushiappas) Additional Couplings (e.g. to Inflaton (Shaposhnikov &

Tkachev)) Low TR models (Gelmini et al., Yaguna et al.)

Produced through a-s oscillations involving off-diagonal elements of mixing matrix (hence no coupling to SM Gauge bosons)

Don’t require finite lepton asymmetry Simplest model: Dodelson-Widrow (DW) mechanism

Standard thermal history No additional couplings required Produces minimal relic density

Alternatives to DW Entropy dilution (Abazajian & Fuller, Abazajian &

Koushiappas) Additional Couplings (e.g. to Inflaton (Shaposhnikov &

Tkachev)) Low TR models (Gelmini et al., Yaguna et al.)Resonant Oscillations

Requires L0 (Shi & Fuller)

Decay modesDecay modes Dominant decay to 3 active neutrinos (s 3a)

Loop-suppressed radiative decay (s a)

Photon Energy E=(ms2-ma

2)/2ms≈ms/2 for ms»ma

For ms~1keV X-rays Use X-ray observations to constrain ms and sin2(2s) (and later, fs for keV SN

DM

Dominant decay to 3 active neutrinos (s 3a)

Loop-suppressed radiative decay (s a)

Photon Energy E=(ms2-ma

2)/2ms≈ms/2 for ms»ma

For ms~1keV X-rays Use X-ray observations to constrain ms and sin2(2s) (and later, fs for keV SN

DM

€

Γs =9α

256 ⋅4π 4sin2(2ϑ s)ms

5 ≈1.38 ×10−22 sin2(2ϑ s)ms

1keV

⎛

⎝ ⎜

⎞

⎠ ⎟5

s−1(Barger et al., Pal & Wolfenstein)

Motivations for keV SN DMMotivations for keV SN DM

Resolution to inconsistencies from CDM halo simulations Central cores in low-mass galaxies (Dalcanton & Hogan) Overpopulation of small-scale satellites (Kauffman et al., Klypin et

al.)

Contribution to unresolved diffuse X-ray background (Abazajian et al.)

Facilitates HI production/star formation Early Reionisation (Mapelli et al., Biermann & Kusenko)

Pulsar “kick” velocities (Kusenko & Segre, Fuller et al.)

Re-generation of Supernova shockwaves (Hidaka and Fuller)

Formation of early SMBH (109M at z≈6.5) (Munyaneza & Biermann)

Baryon asymmetry (Asaka et al.)

Neutrino oscillations (LSND/MiniBoonE require at least 2 light (~eV) SNs) (Goswami & Rodejohann)

Resolution to inconsistencies from CDM halo simulations Central cores in low-mass galaxies (Dalcanton & Hogan) Overpopulation of small-scale satellites (Kauffman et al., Klypin et

al.)

Contribution to unresolved diffuse X-ray background (Abazajian et al.)

Facilitates HI production/star formation Early Reionisation (Mapelli et al., Biermann & Kusenko)

Pulsar “kick” velocities (Kusenko & Segre, Fuller et al.)

Re-generation of Supernova shockwaves (Hidaka and Fuller)

Formation of early SMBH (109M at z≈6.5) (Munyaneza & Biermann)

Baryon asymmetry (Asaka et al.)

Neutrino oscillations (LSND/MiniBoonE require at least 2 light (~eV) SNs) (Goswami & Rodejohann)

Experimental constraints on ms and sin2(2s)


X-rays (Clusters, dSphs, MW, Galaxies, XRB) X-rays (Clusters, dSphs, MW, Galaxies, XRB)

All these sources have similar NH, but different thermal emissions F.O.V and Energy resolution of instruments dictate sensitivity

(Ruchayskiy, arXiv:0704.3215)


Experimental constraints on ms and sin2(2s)Lyman-

Sensitive to small-scale matter perturbations where SN are significantOperates at high-z before non-linear growth erases free-streaming effects

ms >14 keV includes 10% suppression from non-thermal nature of SNRecent calculations imply <ps>/<pa> can be as low as 0.8

ms>11.5 keV (<ps>/<pa>~0.8)

(Abazajian, astro-ph/0511630) (Seljak et al., astro-ph/0602430)

Is Dodelson-Widrow SN DM still permitted?

If fs=1 is excluded, how large can fs be?

DW SN DM for fs=1 (DM=0.24)

€

fs =Ωs

ΩDM

(Yuskel et al., arXiv:0706.4084)

Spectral Analysis of HEAO-1 XRB data


Fit HEAO-1 data to a prescribed model (Gruber et al.)

Add MW and extragalactic (EG) contributions from SN DM (for given ms), correcting for finite energy resolution of HEAO-1 (E/E~0.25)

Vary CXRB, TXRB, ΓXRB and sin2(2s) until 2 worsens by 2 corresponding to a 3 C.L.

Determine sin2(2s) for all ms within range of data

Fit HEAO-1 data to a prescribed model (Gruber et al.)

Add MW and extragalactic (EG) contributions from SN DM (for given ms), correcting for finite energy resolution of HEAO-1 (E/E~0.25)

Vary CXRB, TXRB, ΓXRB and sin2(2s) until 2 worsens by 2 corresponding to a 3 C.L.

Determine sin2(2s) for all ms within range of data

€

ϕ EGruber ≡

d2FEGruber

dΩdE= CXRB exp −

E

TXRB

⎛

⎝ ⎜

⎞

⎠ ⎟

E

60keV

⎡

⎣ ⎢

⎤

⎦ ⎥

−ΓXRB +1

sr−1cm−2s−1



(Boyarsky et al., astro-ph/0512509 )

EG and MW flux from SN DMEG and MW flux from SN DM Extragalactic differential energy flux

Flat, -matter dominated Universe (dm 0.21)

Extragalactic differential energy flux

Flat, -matter dominated Universe (dm 0.21)

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ϕ EEG ≡

d2FEEG

dΩdE= fs

Γγ

4πms

Ωdmρ c

H({ms /2E} −1)

Local differential energy flux from MW

€

H(z) ≈ H0 ΩΛ + Ωm (1+ z)3 , (Ωm ≈ 0.26, ΩΛ ≈ 0.74, H0 ≈ 73 km s−1 Mpc-1)

€

ϕ EMW ≡

d2FEMW

dΩdE= f s

Γγ

4π ms

ρ dm (x,φ)dxl.o.s.

∫ ≡ f s

Γγ

4π ms

Sdm (φ)

€

⇒ R =ϕ E

MWdE∫ϕ E

EGdE∫≈ 0.7

Sdm (φ)

0.01 g cm-2

⎛

⎝ ⎜

⎞

⎠ ⎟~ 1 for typical profiles (away from GC)

X-ray constraints on ms and sin2(2s) X-ray constraints on ms and sin2(2s)

For fs<1 we expect a “rigid” shift in constraints to larger sin2(2s) by 1/fs

€

Γs ∝ fs ms sin2(2ϑ s)

Ly- constraints on ms and sin2(2s) (fs<1)


ms>11.5 keV (fs=1) from limiting suppression of P(k) for k>~Mpc-1

For fs<1 its most appropriate to run a grid of hydrodynamical simulations involving WDM+CDM and relate Ly- power spectrum to parameters.

Alternatively, we can obtain reliable constraints by “rescaling” fs=1 results

Using CAMB (Lewis et al.), we grow perturbations in a WDM(fs)+CDM(1-fs) scenario using a SN relic abundance of

Owing to “pencil-beam” nature of Ly- measurements we use P1D(k)

Determine (ms)min., for fs<1, by invoking P1D(kf, fs<1)=P1D(kf, fs=1) at kf ~2h Mpc-1, where SDSS Ly- data is most sensitive.

Reliable results for fs>0.1 for 1<k_f/Mpc-1<5 (<10% variation).

€

sh2 = β

ms

93.2eV

⎛

⎝ ⎜

⎞

⎠ ⎟

€

P1D(k) =1

2πP3D(k)kdk

k

∞

∫

P(kf,fs)~0.23PCDM(kf,fs=1)



Experimental constraints & Theoretical predictions (2)

DW SN DM excluded for fs=1 DW SN DM permitted for fs=0.2

(2.5<ms/1keV<16, 10-10<sin2(2s)<2.5x10-9)

A

C

E

D

B

F

Theoretical uncertaintiesTheoretical uncertainties SN which are non-resonantly produced have a relic abundance (Asaka et al.)

Accounting for hadronic uncertainties during QCD epoch, best-fit relation between fs, ms and sin2(2s) is

Pushing all errors in the same direction, one either obtains the minimal…

…or the maximal abundances

We conservatively consider these extreme cases to represent a 2 C.L.

SN which are non-resonantly produced have a relic abundance (Asaka et al.)

Accounting for hadronic uncertainties during QCD epoch, best-fit relation between fs, ms and sin2(2s) is

Pushing all errors in the same direction, one either obtains the minimal…

…or the maximal abundances

We conservatively consider these extreme cases to represent a 2 C.L.

€

sh2 = 0.275 F(ms,ϑ α

a= e,μ ,τ )ms

1keV

⎛

⎝ ⎜

⎞

⎠ ⎟2

sin2(2ϑ )

10−7

⎛

⎝ ⎜

⎞

⎠ ⎟

€

log10( f sav.) = 0.20 +1.84 log10

ms

1keV

⎛

⎝ ⎜

⎞

⎠ ⎟+ log10

sin2(2ϑ s)

10−7

⎛

⎝ ⎜

⎞

⎠ ⎟

€

log10( f smin .) = −0.07 +1.74 log10

ms

1keV

⎛

⎝ ⎜

⎞

⎠ ⎟+ log10

sin2(2ϑ s)

10−7

⎛

⎝ ⎜

⎞

⎠ ⎟

€

log10( f smax .) = 0.62 +1.74 log10

ms

1keV

⎛

⎝ ⎜

⎞

⎠ ⎟+ log10

sin2(2ϑ s)

10−7

⎛

⎝ ⎜

⎞

⎠ ⎟

Constraints on the DW scenario (2)

Constraints on the DW scenario (2)

Plot corresponding points (A,B), (C,D) and (E,F) for all fs<1

Plot corresponding points (A,B), (C,D) and (E,F) for all fs<1

0.55<(fs)max.<0.75

Theoretical uncertainties (Quantitative treatment)

Theoretical uncertainties (Quantitative treatment)

Vary fs around fsav. given by best-fit formula.

Adopt a normal distribution of log10(fs) with a s.d. equal to half

the excursion (wrt log10(fsav.) determined by extreme

formulae.

This corresponds to adding a penalty factor to the total 2

with 1 (asymmetric) errors

Vary fs around fsav. given by best-fit formula.

Adopt a normal distribution of log10(fs) with a s.d. equal to half

the excursion (wrt log10(fsav.) determined by extreme

formulae.

This corresponds to adding a penalty factor to the total 2

with 1 (asymmetric) errors

€

2 = χ X−ray2 (sin2(2ϑ s,ms, f s) + χ Ly -α

2 (ms, f s) + η (sin2(2ϑ s,ms, f s)

€

(sin2(2ϑ s,ms, f s) =log10( f s) − log10( f s

av.)

Δlog10( f s)

⎛

⎝ ⎜

⎞

⎠ ⎟

2

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log10( f s) = 0.5 log10( f smax.) − log10( f s

av.)[ ] ( f s > fsav.)

Δlog10( f s) = 0.5 log10( f sav.) − log10( fs

min.)[ ] ( fs < f sav. )

Marginalising 2 wrt fs, ms or sin2(2s), we obtain new constraints…

Constraints on the DW scenarioConstraints on the DW scenario

(fs)max.0.7 (2), (fs)max.=1 (~3)

fs1

fs0.7

Summary & ConclusionsSummary & Conclusions Recent results disfavour keV dominant sterile neutrino dark

matter produced via the Dodelson-Widrow mechanism. Relaxing the presumption that s=dm, we have shown how X-ray

and Ly- constraints can be re-interpreted for s<dm.

Most importantly, we have shown how current data provides a conservative upper bound on the fraction fs of dark matter constituting of sterile neutrinos produced via the DW mechanism.

We obtained the limits fs<~0.7 (2), with fs=1 rejected at ~3.

We found that these limits are robust with respect to the large hadronic uncertainties affecting theoretical predictions.

More sensitive X-ray observations, a better understanding of the systematics in Ly- measurements and a reduction in the theoretical uncertainties all have a crucial role in improving our results.

Recent results disfavour keV dominant sterile neutrino dark matter produced via the Dodelson-Widrow mechanism.

Relaxing the presumption that s=dm, we have shown how X-ray and Ly- constraints can be re-interpreted for s<dm.

Most importantly, we have shown how current data provides a conservative upper bound on the fraction fs of dark matter constituting of sterile neutrinos produced via the DW mechanism.

We obtained the limits fs<~0.7 (2), with fs=1 rejected at ~3.

We found that these limits are robust with respect to the large hadronic uncertainties affecting theoretical predictions.

More sensitive X-ray observations, a better understanding of the systematics in Ly- measurements and a reduction in the theoretical uncertainties all have a crucial role in improving our results.

sterile neutrinos as subdominant warm dark matter

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