Sterile Neutrino Dark Ma/er Dark Ma/er 2014 UCLA February 27, 2014
George M. Fuller Department of Physics & Center for Astrophysics and Space Science University of California, San Diego A take-­‐away message from the experiments is that neutrinos have non-­‐zero rest masses This fact begs the quesCon: Are there sterile neutrino states? |⌫e = cos ✓ |⌫1 + sin ✓ |⌫2
|⌫s ⇥ =
sin ✓ |⌫1 ⇥ + cos ✓ |⌫2 ⇥
If sterile neutrinos mix with acCve neutrinos in vacuum like this, then they are not really sterile !! active neutrino cross section
⇠ G2F E⌫2
“sterile” neutrino cross section ⇥ ⇠ (G2F sin2 ) E⌫2
contrary to what you may have heard . . . Sterile Neutrinos can be Hot, Warm, or COLD Dark Ma/er . . . depending on how their relic densiCes are produced !! Alex Kusenko will talk about various models that produce sterile neutrino dark ma=er Sterile Neutrino Dark Ma/er producKon models see review by Alex Kusenko: Physics Reports 481, 1 (2009) active-active neutrino scattering-induced decoherence
S. Dodelson & L. M. Widrow, Phys. Rev. Lett. 72, 17 (1994)
A. D. Dolgov & S. H. Hansen, Astropart. Phys. 16, 339 (2002)
Largely eliminated by the X-ray observations
But Many Models Are Still Viable . . .
low temperature inflation
M. Shaposhnikov & I. Tkachev, Phys. Lett. B 639, 414 (2006)
Higgs decay and dilution/late-entropy addition
A. Kusenko, Phys. Rev. Lett. 97, 241301 (2006)
K. Petraki & A. Kusenko (2007), arXiv:0711.4646
K. Petraki (20008), arXiv:0801.3470
T. Asaka, S. Blanchet, M. Shaposhnikov, Phys. Lett. B 631, 151 (2005)
G. Fuller, C. Kishimoto, A. Kusenko, A. Patwardhan 2014
lepton number-enhanced decoherence
X. Shi & G. M. Fuller, Phys. Rev. Lett. 83, 3120 (1999)
K. Abazajian, G.M. Fuller, M. Patel, Phys. Rev. D 64, 023501 (2001)
C. Kishimoto & G.M. Fuller, Phys. Rev. D 78, 023524 (2008) arXiv:0802.3377
M. Shaposhnikov, Nucl. Phys. B 763, 49 (2007)
(1) Quantum Mechanical Limit: Dodelson & Widrow 1994 acCve neutrino scaTering-­‐induced de-­‐coherence produces a relic density of sterile neutrinos -­‐-­‐ picks out keV scale rest masses, small vacuum mixing angles (2) Lepton number-­‐driven resonant producKon: Shi & Fuller 1998; Abazajian, Fuller, Patel 2001 Like MSW, iniCal lepton number parCally converted to a relic sterile neutrino populaCon -­‐-­‐ can work for smaller mixing angles, colder sterile neutrino relic energy spectrum -­‐-­‐ sterile neutrinos may allow you to make the lepton number e.g., Asaka & Shaposhnikov , The nuMSM, dark ma=er, and baryon asymmetry , PLB 620, 17 (2005) QCD transiCon 170 MeV (3) Higgs decay; DiluKon: e.g., Asaka, Shaposhnikov, Kusenko (2006); Fuller, Kishimoto, Kusenko, Patwardhan (2014) thermalize or parCally thermalize steriles very early, then dilute them down to a DM relic density -­‐-­‐ can produce relic sterile neutrino populaNons which are CDM for rest masses ~ 1 keV to ~ 10 MeV, with extremely small vacuum mixing angles A heavy sterile neutrino can decay into a light acKve neutrino and a photon. The final state light neutrino and photon equally share the rest mass energy of the iniKal heavy neutrino. Singlet Neutrino RadiaKve Decay Rate αGF2 5
Γγ ≈
m2
4
64 π
[∑ U U
β
1β
2β
]
2
F(rβ )
5
2
,
/
−33 -1 sin 2θ , m s /
≈ 6.8 ×10 s . −10 1.
1
- 10 0- keV 0
€
no GIM suppression for sterile neutrinos F(rβ ) ≈ − 32 + 43 rβ
rβ = ( M
lep
β
MW )
2
A serendipitous coincidence: K. Abazajian, G. M. Fuller, W. H. Tucker, Astrophys. J. 562, 593 (2001) X-­‐ray observatories (e.g., XMM-­‐Newton and Chandra) have greatest sensiKvity for photons with energies between about 1 keV to 10 keV, serendipitously coincident with the expected photon energies from decaying Dark Ma/er sterile neutrinos. Typical lifeKmes against radiaKve decay are some ~1016 Kmes the age of the universe! However, if steriles are the Dark Ma/er, then in a typical cluster of galaxies there could be ~1079 of these parKcles. This could allow x-­‐ray observatories to probe physics at interacKon strengths some 10-­‐14 orders of magnitude smaller than the Weak InteracKon. Chandra X-Ray Observatory
XMM-Newton X-Ray Observatory
Abazajian, Fuller, Tucker 2001 -­‐  look at clusters of galaxies, because that is where the dark maTer is! but these are tough places to look for dark maTer-­‐generated X-­‐ray lines in the keV energy range because there is hot gas with heavy elements with a temperature ~ keV, meaning lots of atomic lines and a fierce X-­‐ray background! ameliorate these issues by stacking spectra for cluster at different redshibs -­‐ smears out instrumental effects H. Yuksel, J. Beacom, C. Watson astro-­‐ph/0706-­‐4084 K. Abazajian 2012 Possible DetecKons two different X-­‐ray astronomy groups see a 3.5 keV line in clusters of galaxies and in M31, and this line is consistent with a dark ma>er decay origin, corresponding to a 7 keV rest mass sterile neutrino with vacuum mixing with acCve neutrinos sin2 2✓ = (2 20) ⇥ 10 11
E. Bulbul, M. Markevitch, A. Foster, R. Smith, M. Lowenstein, S. Randall DetecNon of an unidenNfied emission line in the stacked X-­‐ray spectrum of Galaxy Clusters arXiv:1402.2301 A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi, J. Franse An unidenCfied line in the X-­‐ray spectrum of the Andromeda galaxy and Perseus galaxy cluster arXiv:1402.4119 combined data significance 4.4
Stacked Spectra
Bulbul et al. 7
1
Perseus MOS Background
Perseus PN Background
Stacked MOS Background
Stacked PN Background
PN
-1
(6.7 keV)
MOS
Fe XXVI
(6.97 keV)
Al K
Cu K
(1.49 keV)
1
(8.05, 8.91 keV)
Si K
Zn K
(1.75 keV)
(8.64, 9.57 keV)
PN Background
Cr
Mn
Fe-K
-1
-1
Flux (counts s keV )
Fe XXV
-1
Flux (counts s keV )
10
0.1
0.1
Cr (5.4 keV)
Mn (5.8 keV)
MOS Background
Fe-K (6.4 keV)
0.01
1
2
4
6
8
10
Energy (keV)
5
7
6
Energy (keV)
Figure 3. Left Panel: Stacked XMM-Newton MOS and PN background-subtracted source spectra and particle background spectra of
the full sample. The spectrum of each observation was scaled to the rest frame prior to stacking. The total filtered exposure time was 6
Ms for MOS and 2 Ms for PN. The background MOS (in blue) and PN (in green) spectra show the e↵ect of smearing of instrumental lines,
such as Cr, Mn, Fe and Ni, as well as Al-K and Si-K fluorescent lines. The e↵ect is due to the stacking of background spectra which are
scaled by di↵erent cluster redshifts. Right Panel: Close-up view of 5.0
8.0 keV band of the background XMM-Newton MOS and PN
spectra of the Perseus cluster compared to the stacked XMM-Newton MOS and PN background spectra. The background lines are less
prominent in the stacked background spectra than in the single source background spectra.
Blueshin each spectrum to z = 0 Add the 73 spectra together using weights from the RMFs and ACFs Ms 2 .oThe
f Menergies
OS data; ~2 Gaussian
Ms of PcompoN data the S xvi (2p1 ! 1s1 ), Ca xix (1s1 2p1 ! 1s2 ), and
< E/E~6 < 10
of the
1
nents were allowed to6 vary by up to 5 eV to account for
Ca
(2p1 !c1s
) linesoat
6xx
~8.5 ×
1
0
s
ource c
ounts o
n M
OS; 5
.1 ×
1
0
s
ource ounts n 2.63
PN keV, 3.90 keV and 4.11
residual uncertainties in the gain and in the energies in
keV, respectively, to estimate the flux of the 3.47 keV,
the atomic database. This way, we were able to model
the continuum emission and strong known emission lines
accurately, leaving a clean residual spectrum to search
for any unidentified lines.
We also fit a power-law model in the full band to represent the residual soft proton background contamination
3.51 keV, 3.68 keV and 3.72 keV lines. The best-fit flux
measurements of these S xvi, Ca xix, and Ca xx lines
are given in Table 2.
We assume the relative abundances of S, Ca, Ar, and K
are proportional to their abundances in the solar photo-
1.5
Flux (cnts s keV )
-1
-1
Flux (cnts s keV )
Full Cluster Sample
Bulbul et al. 10
-1
3.57 ± 0.02 (0.03)
0.7
XMM-MOS
Full Sample
6 Ms
3.51 ± 0.03 (0.05)
-1
0.8
0.6
0.02
XMM-PN
Full Sample
2 Ms
1
0
-0.01
0.02
0
-0.02
2
Eff. Area (cm )
-0.02
315
Eff. Area (cm )
2
Residuals
Residuals
0.04
0.01
310
305
300
3
3.2
3.4
3.6
3.8
1020
1000
980
4
3
3.2
3.4
Energy (keV)
Residuals
= 22.8
0.04
FDM =
0
XMM-MOS
Centaurus +
Coma +
Ophiuchus
525.3 ks
3
3.2
3.4
3.6
4
3.8
= 13.9
0.1
0
4
6
-0.1
-0.2
sin 2✓
+1.4 +2.0
=
6.8
1.4 ( 3.0 )
11
10
280
3.8
+1.0
FDM = 3.9+0.6
(
1.0
1.6 ) ⇥ 10
Eff. Area (cm )
285
2
⇥ 10
6
2
2
Eff. Area (cm )
-0.04
+1.8
4.0+0.8
(
0.8
1.2 )
2
0.2
Residuals
2
0.08
3.6
Energy (keV)
650
640
sin2 2✓
+1.7 +2.7
=
6.7
1.0 ( 1.7 )
11
10
XMM-PN
Centaurus +
Coma +
Ophiuchus
168 ks
630
3
3.2
3.4
3.6
3.8
4
Sterile Nu decay line
-7
Do
M 31 X-ray
del
son
&W
idr
ow
-8
-9
2
sin 2θ
UMIN X-ray
-6
-13
Abazajian, K. (2012) Yüskel, H., Beacom, J. F., Watson, C. 1
ms [keV]
Subhalo
counts limit
-12
Tremaine-Gunn
-11
Phase-space limit
-10
10
Horiuchi, Abazajian, K., S., Kaplighat, M. (2014) Horiuchi, Abazajian, K., S., Kaplighat, M. (2014 -7
Do
son
&W
idr
ow
-9
2
sin 2!
M 31 X-ray
del
-8
UMIN X-ray
-6
-13
1
ms [keV]
Subhalo
counts limit
-12
Tremaine-Gunn
-11
Phase-space limit
-10
10
−0.022
−0.022
−2.3
−2.3
+1.4
+1.4
4.64.6
(M31
) ) (3 (3
dof)
(M31
dof)
−1.4
−1.4
15700.2
±±
0.03
0.70.7
(2σ)
... ..
15700.2 33.1/33
33.1/33 3.53
3.53
0.03 < <
(2σ)
+ M31
ONON
- CENTER
+ M31
- CENTER
B LANK
- SKY
B LANK
- SKY
TABLE
I: Basic
properties
of of
combined
observations
used
in in
thisthis
paper.
Second
column
denotes
thethe
sum
of of
exposures
ofof
individual
observaTABLE
I: Basic
properties
combined
observations
used
paper.
Second
column
denotes
sum
exposures
individual
observa2 2
tions.
TheThe
lastlast
column
shows
change
in ∆χ
2 extra
d.o.f.
(position
andand
flux
of of
thethe
line)
areare
added.
The
energies
forfor
Perseus
areare
quoted
tions.
column
shows
change
in ∆χwhen
when
2 extra
d.o.f.
(position
flux
line)
added.
The
energies
Perseus
quoted
in the
restrest
frame
of the
object.
in the
frame
of the
object.
Boyarsky et al. Normalized count rate
[cts/sec/keV]
0.28
0.28
0.26
0.26
0.22
0.22
-2 -2
1!101!10
Data - model
[cts/sec/keV]
0.30
0.30
0.24
0.24
No line
at 3.5
No line
at 3.5
keV keV
Data - model
No line
at 3.5
No line
at 3.5
keV keV
0.32
0.32
[cts/sec/keV]
Normalized count rate
0.100.10
ON-center
M31M31
ON-center
0.34
0.34
line
No No
line
at at
3.53.5
keVkeV
Line
Line
at at
3.53.5
keVkeV
-3 -3
8!108!10
-3 -3
6!106!10
[cts/sec/keV]
[cts/sec/keV]
[cts/sec/keV]
Normalized count rate
1.001.00
[cts/sec/keV]
[cts/sec/keV]
0.36
0.36
ON-center
M31 M31
ON-center
0.01
0.01
-2 -2
1!101!10
-3 -3
8!108!10
-3 -3
6!106!10
-3 -3
4!104!10
-3 -3
2!102!10
0
0
0!100!10
-3 -3
-2!10
-2!10
-3 -3
-4!10
-4!10
-3
-6!10
-6!10-3
1.0 1.0
Data - model
Data - model
Normalized count rate
10.00
10.00
-3 -3
4!104!10
-3 -3
2!102!10
0
0
0!100!10
-3 -3
-2!10
-2!10
2.0 2.0
3.0 3.0
4.0 4.0
5.0 5.0
Energy
[keV]
Energy
[keV]
6.06.0
7.07.0
8.08.0
-3 -3
-4!10
-4!10
3.03.0
3.23.2
3.43.4
3.63.6
Energy
[keV]
Energy
[keV]
3.83.8
4.04.0
6
8
15
Flux x 106 [cts/cm2/sec]
8
s
NFW DM line,
872 kpc
NFWrsDM= line,
rs = 360 kpc
!-model, ! = 0.71,
287 kpc
NFWrcDM= line,
rs = 872 kpc
!-model, ! = 0.71, rc = 287 kpc
Flux x 106 [cts/cm2/sec]
off-center upper limit on-center
NFW,
c = 11.7
off-center
upper limit
NFW, c = NFW,
19 c = 11.7
NFW, c = 19
Flux x 106 [cts/cm2/sec]
Flux x 106 [cts/cm2/sec]
4 Statistical Y-errorbars on the
FIG.
1: Left:
Folded
count
(top)
residuals
(bottom)
MOS
spectrum
central
region
M31.
FIG.
1: Left:
Folded
count
raterate
(top)
andand
residuals
(bottom)
forfor
thethe
MOS
spectrum
of of
thethe
central
region
of of
M31.
Statistical
Y-errorbars on the
4
smaller
than
point
size.
around
keV
is not
added,
hence
group
positive
residuals.
Right:
zoom
onto
line
toptop
plotplot
areare
smaller
than
thethe
point
size.
TheThe
lineline
around
3.53.5
keV
is not
added,
hence
thethe
group
of of
positive
residuals.
Right:
zoom
onto
thethe
line
M31 surface brightness profile
Perseus cluster surface brigtness profile
M31
surface
brightness
profile
Perseus
cluster
surface
brigtness
profile
region.
10
20
region.
NFW DM line, r = 360 kpc
on-center
10
20
15
with
such
a large
exposure
requires
special
analysis
The
observed
brightness
a decaying
DM
line
should
prowith
such
a large
exposure
requires
special
analysis
(as(as
de-de- The
observed
brightness
ofof
a decaying
DM
line
should
pro! ! bebe
scribed
[16]).This
This
analysis
reveal
any
line-like portional
portional
dark
matter
column
density
SDM== ρDM
ρDM
scribed
in in
[16]).
analysis
diddid
notnot
reveal
any
line-like
to to
thethe
dark
matter
column
density
SDM
d%d%– –
residuals
in the
range
3.45−3.58
keV
with
upper
bound integral
integral
along
line
sight
DM
density
distribution:
residuals
in the
range
3.45−3.58
keV
with
thethe
2σ2σ
upper
bound
along
thethe
line
ofof
sight
ofof
thethe
DM
density
distribution:
−7
2
−7
2
flux
being
× 10 cts/cm
cts/cm
/sec.
The
closest
detected
on on
thethe
flux
being
7 ×7 10
/sec.
The
closest
detected
+0.10
+0.10
##
""
2 2 = 4.5) is at 3.67
line-like
feature
(∆χ
keV,
consistent
line-like feature (∆χ = 4.5) is at 3.67−0.05
keV, consistent
−0.05
cts
Ω
fov
cts
Ω
fov
−6−6
FDM≈ ≈
× (1)
3 3
FDM
2.02.0
××
1010
with
instrumental
line.
2 · sec
with
thethe
instrumental
CaCa
KαKα
line.
2 2 × (1)
2
cm
500
arcmin
cm · sec 500
arcmin
# r is29
" " is assumed, the#scale
"to" ##
FIG. 2: The line’s brightness profile in M31 (left) and the Perseus cluster (right). An NFW DM distribution
29 fixed
s
S
10
srs iskeV
keVto
DM
S
10
s
FIG.
2:
The
line’s
brightness
profile
in
M31
(left)
and
the
Perseus
cluster
(right).
An
NFW
DM
distribution
is
assumed,
the
scale
fixed
Combined
fit
of
M31
+
Perseus.
Finally,
we
have
performed
DM
Combined
fit ofvalues
M31from
+ Perseus.
we
performed
its best-fit
[22] (M31) or Finally,
[23] (Perseus)
andhave
the overall
normalization is adjusted to pass through the left-most point.
. .
its best-fit values from [22] (M31) or [23] (Perseus) and the overall normalization is adjusted to pass through
the2left-most
point.
2
!!
500
/pc
τDM mm
a simultaneous
on-center
M31
and
Perseus
datasets
500
MM
/pc
τDM
a simultaneous
fit fit
of of
thethe
on-center
M31
and
Perseus
datasets
DMDM
(MOS),
keeping
common
position
line(in(inthetherestrest(MOS),
keeping
common
position
of of
thethe
line
0.10
frame)
allowing
line
normalizations
different.
frame)
andand
allowing
thethe
line
normalizations
to to
bebe
different.
4
2
6
4
10
5
R200
10
R200
5
2
0
0.2
0
0
0.4
0.6
0.8
0.2 Radius [deg]
0.4
0.6
Radius [deg]
1
0.8
0.4
1
rate
0
0 0.6
0.4
ate
0
0.8
0.6
1
1.2
1.4
1.6
0.8 [deg]
1
1.2
1.4
Radius
Radius [deg]
1.8
1.6
2
1.8
2
Blank sky dataset
Blank sky dataset
0.10
Systematic Uncertainties
Weak line with equivalent width ~ 1 eV
CCD energy resolution ~ 100 eV
XSPEC minimization algorithm
Notoriously difficult to find global minima with line energies
and widths
Effective Area variations:
Systematic uncertainty for nearby clusters
Tension in line energy between MOS and PN
Resolved if flux of Ar XVII DR line is a free parameter, but
then causes K XVIII to have a flux ~10 – 20 times higher than
expected
Abazajian 2014 2
Abazajian 2014 – use ms = 7 keV, sin ⇠ 5 ⇥ 10
11
, lepton number 5 ⇥ 10
4
Other Clusters MOS
ther Clusters PN
erseus (Core-Cut) MOS
erseus (Core-Cut)PN
erseus ACIS-I
erseus ACIS-S
irgo ACIS-I
100
ixing angle measurei↵erent samples used
ing method with the
et cluster at 3.57 keV
gure. The error bars
evel.
of this line should
bright clusters, inores.
trino origin is corarily imply this is
ng a standard cose of a few hundred
ced by oscillations
determined by the
n & Widrow 1994;
utrino with a mix7 ⇥ 10 11 , about
manner. This im-
1.5×10
Astro-H SXS
Perseus, 1 Msec
kT = 6.5 keV, 0.6 solar
z=0.0178
v(baryons) = 300 km/s
v(line) = 1300 km/s
3.62 keV
Ar XVII DR
10
oma+Centaurus+Ophiuchus
OS
oma+Centaurus+Ophiuchus
N
Ca XIX
Ar XVII
Ar XVIII
3.55 keV Line
5×10
ullet Cluster (Boyarsky
al. 2008)
ull Sample MOS
ull Sample PN
Flux (ph cm-2s-1keV-1)
Bulbul et al. Future smoking gun? -­‐-­‐ Astro-­‐H will have ~23
few eV energy resoluCon 3
3.2
3.4
3.6
3.8
Energy (keV)
Figure 14. 1 Ms Astro-H SXS simulations of the Perseus cluster.
The line width corresponds to line of sight velocity dispersion of
1300 km s 1 . The figure shows that the decaying dark matter
line broadened by the virial velocities of dark matter particles will
easily be distinguished from the plasma emission lines which are
broadened by turbulence in sufficiently deep observations of the
Perseus cluster.
addition to the quoted statistical errors. The line is very
weak, with an equivalent width in the full-sample spectra of only ⇠ 1 eV. Given the CCD energy resolution
of ⇠ 100 eV, this means that our line is a ⇠ 1% bump
above the continuum. This is why an accurate continuum
model in the immediate vicinity of the line is extremely
important; we could not leave even moderately significant residuals unmodeled. To achieve this, we could not
rely on any standard plasma emission models and instead
had to let all the tabulated lines free (including their
resolve the Virial width? see Lowenstein & Kusenko Dwarf Spheroidal Galaxies -­‐ not much gas, not many stars, mostly dark maTer! – low X-­‐ray background M. Lowenstein & A. Kusenko Loewenstein & Kusenko (2012)
Fig. 8.— The shaded region in the mst − θ sterile neutrino parameter plane is generally excluded assuming
only the standard cosmological history below the temperature where production by neutrino oscillations