Constraining Sterile Neutrino Warm Dark Matter with Chandra Observations of the Andromeda Galaxy

0.32 MB·English

by  Casey R. Watson

Constraining Sterile Neutrino Warm Dark Matter with Chandra Observations of the
Andromeda Galaxy
Casey R. Watson,1 Zhiyuan Li,2 and Nicholas K. Polley1
1Department of Physics and Astronomy, Millikin University, Decatur, Illinois 62522
2Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138
We use the Chandra unresolved X-ray emission spectrum from a 12′−28′ (2.8-6.4 kpc) annular
region of the Andromeda galaxy to constrain the radiative decay of sterile neutrino warm dark
matter. By excising the most baryon-dominated, central 2.8 kpc of the galaxy, we reduce the
uncertainties in our estimate of the dark matter mass within the field of view and improve the
2 signal-to-noiseratioofprospectivesterileneutrinodecaysignaturesrelativetohotgasandunresolved
1 stellar emission. Our findings impose the most stringent limit on the sterile neutrino mass to date
0 inthecontextoftheDodelson-Widrowmodel,ms<2.2keV(95%C.L.). Ourresultsalsoconstrain
2 alternativesterileneutrinoproduction scenarios atverysmall active-sterileneutrinomixingangles.

n
PACSnumbers: 95.35.+d,13.35.Hb,14.60.St,14.60.Pq
a
J

0
I. INTRODUCTION [66, 67], M33 [68], Milky Way satellite galaxies like the
1
Large Magellenic Cloud [69], Ursa Minor [70, 71], Draco

[72], Wilman I [73], and Seque I [74], as well as unre-
] In nearly all extensions of the Standard Model, the
O solved emission from the Milky Way itself [70, 75–78].
generation of neutrino masses leads to the introduction
C SeeRefs.[13,66,76]andreferencesthereinforamorede-
ofsterileneutrinos,e.g.,[1,2]. Sterileneutrinosmayalso
tailedsummaryandRefs.[79,80]formoregeneralstudies
. play the role of the dark matter, e.g., [3–14] and affect
h of radiative limits.
p a host of interesting cosmological and astrophysical pro-
- cesses,includingtheproductionofbaryon[15–17,20]and Although the original Dodelson-Widrow (DW) non-
o lepton [18] asymmetries, Big Bang Nucleosynthesis [18– resonant sterile neutrino production scenario [3, 6, 44]
tr 20], the evolutionofthe matter power spectrum[21,22], has nearly been excluded by radiative constraints alone,
as reionization [23–31], neutrino oscillations [32, 33], pul- e.g,ms <3.5keV(95%C.L.)[66],andcanaccountforat
[ sar kicks [34–39], and supernovae [40–42]. The degree to most70%ofthedarkmatterat2 σaccordingtoRef.[59],
which sterile neutrinos participate in these processes is recent Suzaku observationsof Wilman I revealeda spec-
2 sensitive to the strength of their interactions with Stan- tral feature at 2.5 keV that was consistent with the ra-
v
7 dard Model particles and their abundance throughout diative decay of a 5 keV DW sterile neutrino [73]. These
1 cosmic history. The creation and exploration of models findingshavebeendiscussedfurtherinRefs.[81,82],and
2 and productionscenariosthat characterizethese proper- wewillreturntotheminSectionsIVandVofthispaper.
4 ties has been [3–7] and continues to be [8–12, 43–56] a In addition to the DW scenario, many other models
1. very active area of research. See Ref. [57] for a review of have been proposed that predict the proper relic dark
1 sterile neutrino properties. matter density even at very small active-sterile neutrino
1 In addition to their rich phenomenology, sterile neu- mixingangles,e.g.,[4,5,13,49,55]. Generalphasespace
1 trinos are also a readily testable dark matter candidate. considerations have also been used to constrain sterile
:
v Todate,theirpropertieshaveprimarilybeenconstrained neutrino production scenarios, e.g., [83, 84].
i in two ways: through X-ray searches for their radiative As a complement to the upper bounds imposed by
X
decays and via observed cosmological small-scale struc- radiative decay constraints, observations of the cluster-
r
a ture,butthe possibilityofdetectionthroughatomicion- ing of cosmological structures on the smallest scales can
ization and nuclear spin flip signatures has also recently set lower bounds on the mass of the dark matter parti-
been discussed [58]. Although the two primary meth- cle. This is because sufficiently light dark matter parti-
odsaregenerallyconsideredseparately,combinedstudies cles would havesuppressedor evenerasedthese smallest
of both radiative and cosmological constraints have also structures by easily propagating (free-streaming) out of
been performed [8, 59, 60]. the shallow gravitational potential wells in which they
The radiativedecaysofpredominantlysterileneutrino formed.
mass eigenstates to predominantly active neutrino mass Currentcosmologicallowerlimitsonm arebasedpri-
s
eigenstatesandX-raysofenergyE =m /2canbe de- marily on measurements of small scale clustering in the
γ,s s
tected by existing X-ray satellites [6]. Current radiative CMB, SDSS galaxy, and Lyα forest flux power spec-
decay limits are based on observations of a long list of tra and gravitational lensing by the smallest structures.
sources,includingtheCosmicX-raybackground[61,62], However,the results of N-body simulations have also re-
nearby clusters such as Virgo [44] and Coma [13, 63], cently been used to set lower bounds on m based on
s
more distant clusters like A520 and A1835 [64] and the requirement that the number of simulated satellite
the bullet cluster [65], nearby galaxies like Andromeda galaxiesequals or exceeds the number of observedMilky
2
Way satellites [85]. also more accurate because we use the Chandra ACIS-I
Of all the cosmologicalconstraints,the Lyα limits are effectivearea,ratherthananaverageflux-to-countratio,
the most sensitive to the difficult-to-characterize, non- to convert calculated sterile neutrino decay signals into
linear growth of baryonic and dark matter structures spectralfeatures. ForMajoranasterileneutrinos,the re-
as well as the specifics of dark matter production, e.g., sulting unresolved emission spectrum requires ms < 2.2
the momentumdistributionofthe darkmatterparticles. keV (95% C.L.) to avoid more than doubling the ob-
There have been significant discrepancies between the served signal in bins of energy E ≥ 1.1 keV. Although
lower limits [44, 86–88, 90, 91] obtained using different the mass-mixing exclusion region we generate with this
data sets and hydrodynamical simulations, as discussed new data set is not vastly more restrictive than the ex-
in, e.g., [13, 76]. Lyα limits are less restrictive for mod- clusion region presented in W06 (see Fig. 4 below), it is
els in which sterile neutrinos behave more like cold dark morerobustforthe reasonscitedabove,andasweargue
matter, e.g., [13, 17, 89]. throughoutthepaper,itwillbedifficulttoimproveupon
the constraints we set here with the current generation
Studies of gravitationally lensed galaxies and QSOs
of X-ray detectors.
have provided comparable lower limits, e.g., m > 5.2
s
keV [92] and m > 10 keV [93], respectively, based In Sec. II, we discuss the basics of the DW scenario
s
on the image distortions caused by the smallest struc- as well as some more recent sterile neutrino models. In
tures. These lensing constraints should improve signif- Sec. III, we discuss the Chandra observations of An-
icantly as data from future submillilensing experiments dromeda, how we generate the unresolved X-ray spec-
become available [94]. Lower bounds based on compar- trumweuseforourconstraints,andhowwecalculatethe
isons of satellite galaxy counts to N-body simulations, darkmattermasscontainedwithintheChandraFOV.In
e.g., m > 13.3 keV (in the DW scenario) [85], are also Sec. IV, we present our analysis of the unresolved spec-
s
similar to the most restrictive Lyα constraints. trum,discussthelimitsweareabletoimposeonthester-
In this paper, we consider the radiative decay limits ileneutrinomassandmixing,andcompareourresultsto
imposedbyChandra [95]observationsofthe Andromeda those of previous studies. In Sec. V we summarize our
galaxy (M31). We choose to focus on Andromeda be- findings and discuss the outlook for future sterile neu-
causeof1)itscloseproximity,2)itssubstantialandwell- trino constraints. Throughout the paper, we assume a
studied dark matter distribution, and 3) its intrinsically flat cosmology with Ωbaryon =0.04, ΩWDM =Ωs =0.24,
low level of X-ray emission. These properties tend to ΩΛ =0.72, and h=H0/100 km s−1 Mpc−1 =0.72.
maximizetheprospectivesterileneutrinodecaysignal(1
and2)andminimizenoise,i.e.,astrophysicalbackground
(3).
The Chandra data set we use in this study also has II. THE STERILE NEUTRINO WARM DARK
several advantages over the XMM-Newton observations MATTER MODEL
ofAndromeda [96] that wereused to constrainthe prop-
erties of sterile neutrinos in Ref. [66] (W06). First, com-
TheradiativedecayrateforMajoranasterileneutrinos
pared to XMM-Newton EPIC, the Chandra ACIS detec-
is [97, 98]
torhasasignificantlylowerandmuchmorestableinstru-
mentalbackground,makingitparticularlywell-suitedfor
extracting low surface brightness, extended X-ray emis- sin22θ m 5
Γ ≃1.36×10−32s−1 s . (1)
sion. Second, using Chandra’s superior angular resolu- s (cid:18)10−10 (cid:19)(cid:16) keV(cid:17)
tion, we are able to remove the emission from a larger
number of resolved, X-ray point sources than would be
The line flux at E = m /2 resulting from the decay
possiblewithXMM-Newton,therebyfurtherreducingas- γ,s s
of the fraction of sterile neutrinos that are within the
trophysical background noise, while excising very little
detector field of view (FOV), NFOV = (MFOV/m ) in a
dark matter from the small excluded regions. Third, the s DM s
halo at a distance D is given by [6, 43, 44]
field of view (FOV) associated with the Chandra spec-
trumweuseinthispaperisover25timestheareaofthe
XMM-NewtonFOVstudiedinW06(a12arcminuteto28 E NFOVΓ
Φ (sin22θ)= γ,s s s ≃1.0×10−17erg cm−2s−1
arcminuteannulusvs.acircleof5arcminuteradius)and x,s 4πD2
therefore probes a significantly larger dark matter mass MFOV D −2 sin22θ m 5
and prospective ν decay signal. The dark matter mass × DM s ,(2)
within this FOV iss not only significantly larger but also (cid:18)1011M⊙(cid:19)(cid:18)Mpc(cid:19) (cid:18)10−10 (cid:19)(cid:16) keV(cid:17)
subject to less uncertainty both because we exclude the
central region of the galaxy,where the dark matter den- where sin22θ characterizes the active-sterile neutrino
sityprofileisleastwellconstrained,andbecausewemake mixing. Dirac sterile neutrinos would produce only half
use of an updated model of the Andromeda dark matter the flux given by Eqn. (2) [97, 98]. To facilitate compar-
distribution based on more recent kinematic data and isons between our work and other results, we will adopt
theoretical considerations. The results of this study are Majorana sterile neutrinos, which have been more com-
3
monly assumed in recent studies, e.g., [67, 76, 78]1.
For a QCD phase-transition temperature of T =
QCD
170 MeV and a lepton asymmetry of L ≃ n /n ≃
baryon γ
10−10, the sterile neutrino density-production relation-
ship for this model is [43]
sin22θ −0.615 Ω 0.5
s
m =55.5 keV . (3)
s (cid:18)10−10(cid:19) (cid:18)0.24(cid:19)
CombiningEqns.(2)and(3)yieldsanexpressionforthe
line flux that is independent of the mixing angle:
Φ (Ω )≃7.0×10−15erg cm−2s−1
x,s s
MFOV D −2 Ω 0.813 m 3.374
× DM s s . (4)
(cid:18)1011M⊙(cid:19)(cid:18)Mpc(cid:19) (cid:18)0.24(cid:19) (cid:16) keV(cid:17)
We note that the density-production relationship pre-
sented in Ref. [48] agrees with Eqn. (3) for sterile neu-
< <
trino masses ranging from 1 keV ∼ ms ∼ 10 keV. The
sterile neutrino mass limits we determine in Sec. IV are
thereforevalidfortherelationshipsinbothRefs.[43]and
[48]. It would also be straightforward to re-evaluate our FIG. 1: Here we show the raw counts associated with the 7
limits on m assuming different density-production rela- ChandraACIS-Iexposureregions(someofwhichareoverlap-
s
tionships, such as the three resonant production models ping) within a 12′−28′ annulus about the center of the An-
dromeda galaxy. Variations in the brightness among these 7
associated with large L [13] or the Shi-Fuller model [4]
regionsaremainlyduetodifferencesinexposuretimes(which
ascalculatedinRef.[55],allofwhichareshowninFig.4
varyfrom 5ksto20ks)ratherthanintrinsicvariationinthe
below.
emission (see text). We have also included an ACIS-I image
ofthecentral12′ toillustratetheextentoftheX-rayemission
from hot gas and point sources that we have eliminated by
III. PROPERTIES OF ANDROMEDA excising the bulgeof thegalaxy from ourFOV.
A. X-ray Data
and 2902) have effective exposure times of ∼5 ks, while
To detect or place the most restrictive constraints on the other two observations have longer exposure times
radiatively decaying dark matter, it is critical to mini- of 8 ks (ObsID 7067) and 20 ks (ObsID 11256), respec-
mize the X-ray background from baryonic sources, such tively. Each 17′x17′ ACIS-I region covers 11.4% of the
as diffuse hot gas and X-ray binaries. In M31, both the 12′−28′annulus,andthenon-overlappingpartsofthese7
diffuse hot gas [99, 100] and X-ray binaries [101] exhibit pointingscollectivelycover∼35%. Weaddresssampling
a relatively steep radial distribution toward the galactic bias later in this section, pointing out that the co-added
center, suggesting that we can optimize the dark mat- spectrumfromtheselectedobservationsprovides,ifany-
ter signal to baryonic noise ratio by avoiding the inner thing, an overestimate of the X-ray emission from the
regions of the galaxy. Although most existing Chandra entire 12′−28′ annulus.
observations of M31 have been aimed toward the inner We obtained and re-processed the archival data using
bulge, we did find seven observations that were aimed CIAOversion4.2andthecorrespondingcalibrationfiles.
toward the outer bulge/disk regions and were therefore We followed the standard procedure of data reduction,
morewell-suitedforourpurposes. Allsevenobservations e.g., as described in Ref. [99]. Briefly, for each observa-
used the Advanced CCD Imaging Spectrometer (ACIS) tion, we (i) filtered time intervals of high particle back-
I-array as the primary detector, with a 17′x17′ field of ground, (ii) detected and removed discrete sources, (iii)
view (FOV). The positions of these observations relative extractedaspectrumfortheunresolvedX-rayemissionin
toanannulusofinnerradius12arcminutesandouterra- the 0.5-8keV rangeand generatedcorrespondinginstru-
dius 28 arcminutes (12′−28′ ≃2.8−6.4 kpc at D ≃ mental response (rmf and arf) files, and (iv) extracted
M31
0.78±0.02 Mpc [102, 103]) are shown in Figure 1. Five a fiducial instrumental background spectrum, using the
ofthesevenobservations(ObsIDs1576,1584,2899,2901 “stow background data” that has been calibrated with
the10-12keVcountrate. Inafinalstep,weco-addedthe
sevenspectra and generatedexposure-weightedresponse
files,usingtheFTOOLaddspec. Suchaprocedureisap-
1 ThedecayrateequationgiveninRef.[76]isforMajoranarather propriate, since the spectra were extracted from nearly
thanDiracsterileneutrinos. identical detector regions.
4
Since the effective area A (E) of ACIS is known to that for our FOV, CDM models predict more conserva-
eff
decreasegraduallywithtime,itisimportanttonotethat tive ΣFOV values than cored, WDM models. Because
DM,M31
these seven observations were taken over a time span of WDM models are less centrally concentratedthan CDM
9years. ByusingaweightedA (E)associatedwiththe models, they are constrained to predict higher densities
eff
co-added spectrum in our analysis below, we are able to at larger radii in order to reach agreement with the to-
gauge the mean sensitivity ofthe detector over this time tal mass of a given halo. For instance, within the radial
interval. Additionally, we note that the degradation of limits of our FOV(2.8-6.4 kpc), the dark matter density
thedetectormainlyaffectsenergiesbelow1keV,andour givenby the Burkertprofile for M31 [106] with the com-
data set has very little constraining power at these low monly adopted parameter values (as in, e.g., Ref. [67])
energies, as we will show. is 17%−29% higher than that of the KZS profile and
Itisalsonoteworthythattheobservedfluxvariesmod- 18%−41% higher than that of the SBB profile. There-
estlyamongthesevenobservations,withinafactorof1.5 fore, despite the fact we are constraining a WDM can-
of the mean values associated with the co-added spec- didate in this paper, we chose the SBB profile over a
trum. This is a natural result, since the observations WDM profile in the interest of providing a conservative
sampleddifferentregionsoftheouterbulgeandthedisk. dark matter mass estimate.
We note, however, that the sampled regions mostly cov- Because of Chandra’s excellent angular resolution, we
ered the southeastern half of the disk – where the unre- lose less than 5% of ΣFOV due to the excision of
DM,M31
solvedX-rayemissionishigherthanthatfromthenorth- point sources. However, to be conservative, we use only
easter side, primarily due to the tilt of M31’s galactic 0.95 ΣFOV forΣFOV inEqns.(7)and(9)todetermine
DM,M31 DM
plane [99]. This sampling bias means that the co-added the prospective sterile neutrino signals in the figures be-
spectrum we use represents an upper limit on the mean low, and we ignore the contribution from the fraction of
fluxwithinthe12′−28′annulus-preciselywhatweneed the Milky Way dark matter halo within the FOV.
to set a robust upper limit on the mass of the sterile
neutrino. Finally, we note that a correction factor of
(0.114)−1 has been applied to the data shown in Fig. 2
IV. CONSTRAINING STERILE NEUTRINO
to account for the fact that the co-added spectrum from DECAYS
the 7 archived observations represents 11.4% of the pro-
jected area of the 12′−28′ annulus.
In Fig. 2, we show the unresolved emission spectrum
from the inner 12′ − 28′ of Andromeda. To calculate
the ν decay signals, we assume that sterile neutrinos
B. Dark Matter Enclosed within the Chandra Field s
comprise all of the dark matter, i.e., Ω = Ω = 0.24,
of View s DM
andevaluateEqn.(4)basedon95%oftheΣFOV value
DM,M31
given in Eqn. (5). We then convert the sterile neutrino
The dark matter halo of M31 has been studied exten-
decay fluxes to the same units as those of the measured
sively. Klypin, Zhao and Somerville (KZS) [104], for in-
spectrum (Counts/sec/keV)as follows:
stance, used a variety of kinematic data to determine its
dark matter density profile, ρ . Using more recent
DM,M31 dN Φ (Ω ) A (E )
data and a more accurate baryonic mass profile, Seigar, γ,s (Ω )= x,s s eff γ,s
s
dE dt (cid:18) E (cid:19)(cid:18) ∆E (cid:19)
Barth and Bullock (SBB) [105] have updated the pro- γ,s γ,s
file found by KZS. When we integrate the SBB model of =6.7×10−2 Counts/sec/keV Aeff(Eγ,s)
ρDM,M31 over the volume, VFOV,M31, associatedwith the (cid:18) 100 cm2 (cid:19)
pwreofijencdtiothnaotfththee1C2′h−an2d8r′aanFnOuVlusalcoonngtatihnes:line of sight, × ΣFDOMV Ωs 0.813 ms 1.374, (7)
(cid:18)1011M⊙Mpc−2(cid:19)(cid:18)0.24(cid:19) (cid:16) keV(cid:17)
ΣFDOMV,M31 ≃(0.8±0.08)×1011M⊙Mpc−2;
where1erg/E =1.6×109(E /keV)−1 givesthenum-
MDFMOV,M31 ≃(0.49±0.05)×1011M⊙, (5) ber of Countsγa,sssociated withγ1,serg at energy E and
γ,s
A (E )and∆E aretheeffectivearea2andspectralen-
where eff γ,s
ergy resolution of the Chandra ACIS-I detector, respec-
ρ (|~r−D~|)dV tively. To realistically simulate detected sterile neutrino
DM FOV
Σ = (6)
FOV Z r2 decay “line” fluxes in Fig. 2, we use a Gaussiancentered
at E =m /2 with a FWHM of ∆E =E /15, a con-
γ,s s γ,s
is the dark matter column density within VFOV, and the servative estimate of the energy resolution of ACIS-I in
dark matter mass within VFOV is defined by MDFMOV = imaging mode3.
D2ΣFOV. (See W06 for further details).
DM
In addition to being based on more contemporary
data and theoretical considerations, the SBB value for
ΣFDOMV,M31 is also more conservative: less than 85% of 2 http://cxc.harvard.edu/proposer/POG/html/ACIS.html
the KZS estimate for this annulus. We further note 3 http://heasarc.nasa.gov/docs/cxo/cxo.html
5
TABLE I: The Table shows the distance to Andromeda, the
angular range, ∆θFOV, of the annular field of view (FOV)
probed by the Chandra observations, the dark matter col-
umn density, ΣFDOMV, enclosed within the FOV (Eqn. 5), and
the(95% C.L.) upperboundson ms for Diracand Majorana
sterile neutrinos.
Galaxy Name Andromeda(M31)
Distance (Mpc) 0.78±0.02
∆θFOV (arcminutes) 12′−28′
ΣFDOMV/1011M⊙Mpc−2 0.8±0.08
mDs (keV)(95% C.L.) 2.4(Dirac)
mMs (keV) (95% C.L.) 2.2(Majorana)
A. DW Sterile Neutrino Mass Limits
Todeterminethemasslimitimposedbytheunresolved
emission spectrum of Andromeda, we find the first bin
of energy E = m /2 for which the sterile neutrino
γ,s s
decay signal (Eqn. 7) at least doubles the amplitude of
FIG.2: HereweshowtheChandraunresolvedX-rayspectrum
the measured spectrum in that bin, ∆F:
emittedfroma12′−28′annularregionaboutthecenterofthe
dN Andromedagalaxy(solid)andthefirststatisticallysignificant
γ,s
dEγ,sdt(Ωs)≥∆F. (8) νasndde1c.a2ykpeVeak(rse(dd)a,swhhedic)haetxEclγu,dse=mmMss,l>im/22.2=ke1V.1(kMeaVjo(rbalnuae))
The resulting limits: mM > 2.2 keV (Majorana) and and mDs > 2.4 keV (Dirac), respectively (95% C.L.; Eqn. 8).
s As a gauge of the statistical significance of our limits, we
mD > 2.4 keV (Dirac), which are shown in Fig. 2 and
s haveincluded the(1 σ) Poisson error barson theunresolved
TableI,aremuchmoresignificantthanthe95%C.L.de-
emission spectrum data points. As a point of comparison
fined by the (1 σ) Poisson error bars on the measured tothepotentialdetectiondiscussedinRef.[73],wealsoshow
points. (For this data set, Eqn. (8) is equivalent to thedecaysignaturethatwouldbeproducedifthedarkmatter
>∼ 4 σ). However, because we do not have a precise un- within the 12′−28′ region of Andromeda were composed of
derstanding of the features of the unresolved emission 5keVsterileneutrinos(green,dot-dashed),apossibility that
spectrum, whichoriginatefromsome combinationofhot is strongly excluded by thedata.
gas, unresolved stellar sources, sky and detector back-
grounds,andpossiblysterileneutrinodecay,wechoosea
limitingcriterionthatwouldremainrobustevento100% were statistically consistent with sterile neutrino decay.
level fluctuations in the data. (See W06 [66] for a more We found that this was the case for the Ne IX peak at
detailed discussion). 1.07 keV. In particular, when we assumed that the Ne
IX peak was a sterile neutrino decay line superposed on
a continuum backgroundcharacterizedby the mean flux
B. Examining Possible DW Sterile Neutrino Decay valuesofthebinstotheleftandrightofthepeakenergy,
Signatures we found that it was best fit by the decay signature of a
2.13 keV Majorana sterile neutrino (see Fig. 3).
There are a large number of atomic emission lines This exercise underscores both the spectral resolution
at energies just below our exclusion limit, i.e., Eγ,s<∼ 1 and amplitude issues. If Andromeda’s dark matter halo
keV. Differentiating between these features and anoma- were actually composed of 2.13 keV sterile neutrinos,
louslineswillbedifficultifnotimpossiblegiventhespec- they would produce a decay signature at 1.065 keV, but
tralresolutionofcurrentdetectors. Thediminishingam- this is clearly indistinguishable from the 1.07 keV Ne IX
plitude of sterile neutrino decay signatures at lower en- feature with the detectors aboard Chandra. If the sterile
ergies, dN ∝ E1.374 (Eqn. 7) further exacerbates this neutrinoswereofevenlowermass,theamplitudeoftheir
dEdt γ,s
problem. Even with a data set such as ours, with a fa- decay signatures would be dwarfed among the thicket
vorably high ratio of FOV dark matter to astrophysical of sub-keV atomic lines, and higher spectral resolution
background, prospective sterile neutrino signals become would become indispensible if we were to have any hope
comparable to or dwarfed by atomic line features at en- of finding them. One of the few options available in the
ergies just below 1.1 keV. absence of such advances is to consider anomalous line
To illustrate this point, we examined whether or not ratios, as in Ref. [107], but doing so requires extremely
any of the atomic emission lines below 1.1 keV in Fig. 2 precise knowledge of chemical abundances, plasma tem-
6
FIG. 3: Here, to illustrate how difficult it is to distinguish
betweenatomicandanomalouslinefeatureswith currentde-
tectors, we show the statistical consistency of the 1.07 keV
Ne IX emission peak (Chandra data points in black) and the FIG. 4: Here we present constraints on ms as a function of
decaysignatureofa2.13keVMajoranasterileneutrino(blue, mixing angle, sin22θ, assuming that all dark matter is com-
shadedregion). Thelightbluebandshowsthe1σuncertainty prised of sterile neutrinos (Ωs = 0.24). For L ≃ 10−10, the
range associated with theChandra data. thick, solid line corresponds to ΩDsW = 0.24 ±0.04 in the
Dodelson-Widrow (DW) scenario (Eqn. 3), while the region
to the right corresponds to ΩDsW > 0.28. Three density-
perature, etc. of the region(s) of the target galaxy being production relationships associated with Ωs = 0.3 and (left
examined. Tomakeprogresswithoutsuchcomplications, to right) L = 0.1, 0.01, and 0.003 are also shown (dotted)
particularly at Eγ,s<∼ 1 keV, a new generation of much [13],asistheShi-Fullerdensity-productionrelationshipcom-
higherspectralresolutiondetectorsisrequired,aswedis- putedin Ref. [55] (dashed). The three previousradiative de-
cuss further in the Sec. V. cay upper limits (all 95% C.L.) are based on Integral mea-
surements of the unresolved X-ray emission from the Milky
Wayhalo[77,78],HEAO-1andXMM-Newtonobservationsof
theCosmicX-rayBackground(CXB)[61],andthemoststrin-
C. Exclusion Regions in the Mass-Mixing Plane
gentconstraints[66]fromthemanylimitsimposedbynearby
galaxiesandclusters[13,44,63,66,69,70,76]. Themagenta
To determine the region of the ms − sin22θ (mass- line shows therecalculated boundaryof thisexclusion region
mixing)plane(Fig.4)thatisexcludedbytheunresolved for Majorana sterile neutrinos (see text), allowing for direct
X-ray spectrum of Andromeda, we convert Eqn. (2) to comparison between our results and those of Ref. [66]. The
Counts/sec/keV: mostrestrictiveradiativedecaylimits,from thepresentwork
(also 95% C.L.), are based on Chandra observations of the
dN Φ (sin22θ) A (E ) Andromedagalaxy.
γ,s sin22θ = x,s eff γ,s
dE dt (cid:18) E (cid:19)(cid:18) ∆E (cid:19)
γ,s (cid:0) (cid:1) γ,s
A (E )
=9.8×10−5 Counts/sec/keV eff γ,s nos. The most restrictive region, which was determined
(cid:18) 100 cm2 (cid:19)
by comparing the Chandra unresolved X-ray spectrum
ΣFOV sin22θ m 3 to the Majorana sterile neutrino decay flux, is shown in
× DM s , (9)
(cid:18)1011M⊙Mpc−2(cid:19)(cid:18)10−10 (cid:19)(cid:16) keV(cid:17) Fig. 4. The “indentation” of our exclusion region at the
highestmassescomes aboutbecause the effective areaof
and adopt the analog of Eqn. (8) as our exclusion crite- theACIS-Idetectorfallsevenmoresteeplythanthespec-
rion: traldata at the highestphoton energies. As discussedin
dN the conclusion, a new instrument with a much larger ef-
γ,s sin22θ ≥∆F. (10) fective area and superior spectral energy resolution will
dE dt
γ,s (cid:0) (cid:1) be required to dramatically improve upon the radiative
Just as we found two mass limits, we also derived two decay constraints presented here.
exclusion regions for Dirac and Majorana sterile neutri- In addition to our new Andromeda bounds, (the dis-
7
tinct parts of) three previously determined radiative de- inwhichΩ ∼0.3canbegeneratedatverysmallmixing.
s
cayexclusionregionsarealsoshowninFig.4. Theupper Sterile neutrinos that are, e.g., resonantly produced in
exclusionregionisbasedonIntegralmeasurementsofthe the presence of a large lepton asymmetry (L ≫ 10−10),
unresolvedX-rayemissionfromtheMilkyWayhalo[77]. e.g., [4, 5, 13, 55] or created via Higgs decays [49] are
We note that these results were corroborated by a very still viable. However, the combination of our X-ray con-
similarlaterstudy [78]. Thesecondexclusionregionwas straints with those from nearby sources are also able
derived by analyzing HEAO-1 and XMM-Newton obser- to partially restrict the L = 0.003 resonant production
vationsoftheCosmicX-rayBackground(CXB)[61]. The model [13] and the Shi-Fuller model [55] for sterile neu-
thirdregionrepresentsthemoststringentconstraints[66] trino masses in the 10 to 24 keV range (Fig. 4), and the
(W06) from the many limits imposed by nearby galaxies IntegralmeasurementsoftheMilkyWayhalo[77,78]ex-
and clusters [13, 44, 63, 66, 69, 70, 76]. We note that clude all the alternative production scenarios shown in
if we were to recalculate the exclusion region derived in Fig. 4 above m =40 keV.
s
W06 [66] for Majorana rather than Dirac sterile neutri- Even without cosmological small scale structure
nos, the boundary of the exclusion region would remain bounds, the DW scenario remains viable only between
the same (the magenta line shown in Fig. 4). This is the Tremaine-Gunn bound [108] and our limit from this
because we would not only need to multiply Φx,s by a work, 0.4 keV < ms < 2.2 keV, which interestingly falls
factor of 2, we would also have to change the overly op- within the range of dark matter particle masses that
timistic estimate of the spectral energy resolution used best explains the core of the Fornax Dwarf Spheroidal
in that paper (∆E = E/30) to the more realistic value galaxy[109]. Thisresultunderscorestheneedtocontinue
used in this analysis (∆E =E/15). Since dNγ,s ∝ Φx,s to carefully and independently pursue all possible con-
dEγ,sdt ∆E
(Eqn. 9), the factors of 2 offset. straintsonsterileneutrinoproperties. However,asnoted
Boyarsky et al. [67] also conducted a very thorough above,becauseofthedecreasingsterileneutrinosignalat
analysisofanannular(XMM-Newton-observed)regionof lowerms valuesandthelargenumberofatomicemission
<
Andromeda (5′−13′). Unfortunately, because of XMM- featuresatenergies∼ 1keV,itwillbedifficulttoimprove
Newton’s poorer spatial resolution, they were forced to upon the 2.2 keV limit we have presented here with ex-
excise almost one fourth of the field of view (∼ 23%) to istingX-raydetectors. Oneofthe mostpromisingroutes
remove the emission from point sources, thereby sacri- towardimprovedradiativeconstraintsincludestheuseof
ficingpotentiallysignal-producingdarkmattertoreduce much higher spectral resolution instruments than those
theastrophysicalbackground. Asaresult,theunresolved currently available, as discussed, e.g., in Refs. [76, 110–
emissionspectrumtheygeneratedprobedamuchsmaller 112]. The International X-ray Observatory (IXO4), for
dark matter mass than the Chandra unresolved X-ray instance,whichisscheduledforlaunchin2021,willhave
spectrum we consider here, and their limits are corre- a FOVcomparable to Chandra detectors (∼ 18’for pho-
spondingly less restrictive (m <4 keV). ton energies ranging from 0.1-15 keV), but ∼ 100 times
s
their effective area, ∼ 10 times their spectral resolution,
and ∼ 10 times lower instrumental background. Based
V. CONCLUSIONS onthese specifications, a megasecondobservationof An-
dromedawithIXOwillhavethecapacitytofullytestthe
4alternativesterile neutrinoproductionscenariosshown
In this paper, we used the Chandra unresolved X-ray
in Fig. 4 overthe entire rangeof mass-mixing parameter
spectrum of the Andromeda galaxy (M31) to improve
space for which they remain viable [111].
the radiative decay constraints on sterile neutrino warm
dark matter. Assuming either the model described in
Refs. [5, 6, 43, 44] or Ref. [48], our analysis requires
m < 2.4 keV (95% C.L.), in the least restrictive case
s Acknowledgments
(Dirac sterile neutrinos). Because many recent papers,
e.g., [67, 76, 78] have assumed Majorana sterile neutri-
nos, we quote the Majorana limit: We thank M. Garcia, S. Murray, and Q.D. Wang,
theprincipalinvestigatorsresponsibleforconductingthe
m <2.2 keV (Majorana; 95% C.L.) (11) Chandraobservationsof M31usedin this work. We also
s
thank JohnBeacomandHasanYu¨kselfor extensive and
asourlowerboundfortheDWscenario,sothatcompar- veryhelpfuldiscussions. CRWandNPacknowledgesup-
isons to other studies can be made on equal footing. portfromthe Millikin University Departmentof Physics
Most of the currently available sterile neutrino mass- and Astronomy. ZL acknowledges support from SAO
mixing parameter space remains open only for scenarios grant GO0-11098B.
4 http://ixo.gsfc.nasa.gov
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