Observational Consistency and Future Predictions for a 3.5 Kev ALP to Photon Line

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Observational consistency and future predictions for a 3.5 keV ALP to photon line

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Please note that terms and conditions apply. JCAP04(2015)013 hysics P le ic t ar doi:10.1088/1475-7516/2015/04/013 strop A G), no observable signal is possible. For ﬁelds at the µ . Content from this work may be used 3 20 pc, reconciling the results from the Chandra and XMM-Newton osmology and and osmology C z > 1410.1867 dark matter theory, axions, galactic magnetic ﬁelds, X-rays

Motivated by the possibility of explaining the 3.5 keV line through dark matter rnal of rnal Article funded byunder SCOAP the terms of the Creative Commons Attribution 3.0 License .

ou An IOP and SISSA journal An IOP and Rudolf Peierls Centre for1 Theoretical Keble Physics, Road, University of Oxford, Oxford, OX1E-mail: 3NP, U.K. , [email protected] , [email protected] , [email protected] , [email protected] [email protected] Any further distribution ofand this the work must title maintain of attribution the to work, the author(s) journal citation and DOI. X-ray telescopes. Thenon-observation of dark the matter 3.5 to keVfor line ALP the in to stacked line galaxy flux photon spectra.3.5 in scenario keV We galaxies also further line and explore in naturally suggest predictions this predicts a model. the set of galaxiesKeywords: that is optimised for observing the ArXiv ePrint: high range of observational estimatesit (a is pervasive poloidal possible mGin to field the generate over galactic the sufficient centre. centralfrom 150 signal the In pc) to region this with explain scenario, recent the galactic observations centre of line a signal 3.5 comes keV predominantly line decaying to axion-like particles thatconversion subsequently for convert sightlines to passing photons,the within we galactic 50 study pc centre ALP-photon magnetic ofof the field observational galactic which estimates centre. is (10–100 highly Conversion depends uncertain. on For fields at low or mid-range Received November 7, 2014 Revised March 12, 2015 Accepted March 18, 2015 Published April 9, 2015 Abstract. Pedro D. Alvarez, JosephM.C. P. David Conlon, Marsh Francesca and V. Markus Day, Rummel J Observational consistency and future predictions for a 3.5photon keV line ALP to JCAP04(2015)013 5 3 4 . 3 ∼ E – 1 – model in other galaxies 17 scenario5 γ γ photon scenario3 → → a a → → → at the centre of the Milky Way 10 γ ALP → → 55 keV, with no apparent astrophysical origin. The line was observed . a 3 → ∼ a E γ → → a These papers have triggered many subsequent observational searches for further The 3.5 keV line was first observed by two distinct groups, using the detectors of two 2.1 DM 4.1 ALP4.2 to photon conversion Predictions probability 4.3 for XMM-Newton and Sensitivity Chandra to model parameters 5.1 Observational5.2 hints and constraints Predictions for the DM 13 11 15 16 2.2 2.3 Predictions of the DM 3.1 Observational3.2 searches for the Electron 3.53.38 density keV line from Magnetic the field9 galactic6 centre keV line emission. In [3], a search was performed in the spectrum of Chandra observations with both the MOS andin PN the Perseus cameras cluster on using theIn both XMM-Newton [2], ACIS-I instrument, a and and ACIS-S line also configurations at(using reconfirmed on very a the similar distinct Chandra energies set satellite. was ofof also XMM-Newton the observed observations Andromeda in than galaxy the in (M31). outskirts [1]) of and the also Perseus in cluster the central region 1 Introduction Determining the nature and propertiesof of dark contemporary matter is high-energy oneof physics. of the dark most Among significant matter challenges thedominated is astrophysical variety the objects. of search strategies Suchof for dark lines for matter unidentified could detecting particles emission arise inthat signs in which lines the the the in final recent two-body state detection the decay/annihilation containsof of a spectra galaxy photon. an clusters of unidentified Hence, and dark it emission the is line matter Andromeda not at galaxy surprising has 3.5independent generated keV satellites, much in interest. XMM-Newton thephysical and X-ray background spectrum Chandra. of a After stackedemission sample carefully line of at subtracting galaxy the clusters, reference astro- [1] found an additional Contents 1 Introduction1 2 The dark matter 5 Searching for the 3.5 keV line in other galaxies 6 Conclusions A List of nearly edge-on spiral galaxies with long X-ray exposures 21 16 20 3 The Milky Way6 centre 4 Dark matter JCAP04(2015)013 and 1 keV σ . 7 ∼ – 2 – under the most conservative assumptions about σ (or 3.3 σ (1) Mpc) and support substantial conversion probabilities, while regular O support for such a line, and questioned the existence of an unexplained line σ observed with XMM-Newton is above the upper bound set by non-observations 2 for Chandra and XMM-Newton samples respectively. spheroidals and stacked galaxies. Our focus here is on the scenario proposed in [10] — which we elaborate on below — As these same limits apply directly to any model in which dark matter decays directly Furthermore, reference [4] also challenged the existence of a line in M31 (claimed in [2]), Less controversial, yet equally important, are the null results reported from searches for σ 2. A signal is observed in the spectrum of M31, but not in other galaxies. 1. A signal is produced in galaxy clusters, but is absent in the spectrum of dwarf which can explain both these features. In this scenario, dark matter with mass to the 3.5decaying keV directly photon, to these photons.in results [1] The appear and challenge [2] fatal for is any to to dark all explain matter why, models interpretation consisting of the of data dark matter of the centralrecently, region two further of analyses the ofbeen the Milky carried galactic out Way, centre4,5]. [ finding spectrumin using These no XMM-Newton interpretations. papers evidence data find have Both of mutuallyreference consistent analyses such4] [ results, argue find line but that differ evidence emission.keV, this significantly for while line a More the should line be authorsinterpretation, attributed around of while to 3.5 reference agreeing K keV.allow [5] XVIII that The for find emission definitive the authors at that exclusion complicated of 3.47per the of and arcmin galactic astrophysical line 3.51 interpretations. centre is In environment consistent both with does analyses, a the not line dark flux matter the galactic dark matterin column [9], density). a However, searchXMM-Newton no for data line the of signal 3.5 galaxies. wasneutrino keV observed. No line interpretation evidence was of Similarly, of performed the11.8 a in line line large suggested at stacks 3.5 in of keV [1] archived was Chandra was found, and found and to the be sterile ruled out at 4.4 has a predominant decayto channel a to 3.5 very keVastrophysical light ALP magnetic axion-like line. fields, particles By a (ALPs),and photon itself thus coherent line this astrophysical giving can line magnetic rise be fields. isover generated ‘invisible’, The large in magnetic but scales regions fields as ( in with ALPs galaxy relatively convert clusters large into are present photons in finding only 1 from clusters, arguing thatline by at including 3.51 K keV, XVIIIsystematic no uncertainties. lines significant excess at In around 3.47 response,lower 3.5 and the significance keV authors 3.51 of could of the keV be 3.5 reference andinappropriately established keV [2] a narrow line after pointed Cl fitting for allowing out XVII interval the for in ofindex M31 [6] analysis 3–4 of that in keV, the the 4] [ resulting power wasIn in due law reference a to background [7], relatively a and the poorer restrictionarguing authors to an fit that an of inevitably they for1] [ relied the lower upon robustly significance incorrect disagreed atomic for with data the and the inconsistent line analysisthe spectroscopic signal. of modelling. line cluster in data galaxies inspheroidal [ 4], galaxies other were than observed M31 usingmatter and XMM-Newton targets as data. the they Milky Dwarf havesterile galaxies Way. high neutrino are dark In classic interpretation matter [8], dark densities ofwas a and the ruled low stacked background results out sample light. of at of Under [1], dwarf a the a level signal of of 4.6 the strength reported in1] [ with Chandra in]. [3 JCAP04(2015)013 , . ψ is ψ µν m y νF , which µν a σ † , where ψ 1 Λ ¯ Lψ † yH are the gamma matrices of spinor µ γ ) and unusually coherent (with no evidence ] where through the effective operator ν is the lepton doublet of the Standard Model. ν , γ L scenario and that have been observed by either µ – 3 – random γ γ [ B 4 1 photon scenario → ∼ = a → reg µν B → σ is the electromagnetic field strength. A frequently considered and a neutrino ALP to be a right-handed sterile neutrino with a Majorana mass µ γ A ψ → ν ∂ is the Higgs field and − ) scenario of [10] in section2. In section3 we review X-ray observations (10) kpc scales. γ ν H O A → model. µ ∂ a γ a = → → → µν a F → Among galaxies, central observations of edge-on spiral galaxies represent the most at- Following its introduction in [10], this scenario has been analysed in more detail for the This paper is organised as follows. We start by reviewing the dark matter to ALP to This model was first proposed in [10] to explain the morphology of the signal observed in While the 3.5 keVmass line of — the if darkrelevant indeed decay matter caused channels. particle, by it For decaying example, does dark if matter not the — by dark may itself determine matter provide the particle information is on a its fermion, spin denoted and subsequently converts into X-ray photons in the presence2.1 of astrophysical magnetic DM fields. it may decay intoHere a Λ photon is a (large)algebra. mass scale and case in this category isand for a mixing with thea Standard Yukawa coupling, Model neutrinos induced by an operator Chandra or XMM-Newton. 2 The dark matter In this section,duced we by review dark matter the particles scenario decaying proposed into an in axion-like particle [10] (ALP), in denoted which the 3.5 keV line is pro- tractive targets, as the regularand, disk for magnetic central field observations, is orthogonalgest both that to M31 coherent the is on particularly line the attractivefield of scale among is edge-on of sight. both spiral the Observational galaxies, unusually galaxy studies as large the [11] (with regular sug- magnetic case of the Milky Wayand halo (excluding non-cool-core the clusters central region)this in in scenario [13]. [12] to and the The for observationallyclarify interesting the objectives its region case predictions of of of for the cool-core the Milky observations paper of Way centre are other and galaxies. to tophoton further extend (DM the study of galaxies and dwarf spheroidals giveare rise only to present much on weaker photon lines as theirgalaxy magnetic clusters fields in [1], whichsignal is found itself in in [1] tension is withinferred direct stronger from dark in the matter the full decay Perseus 73from to cluster photons. cluster the — sample. by The central up The cool toclusters signal core a in — factor region Perseus of Coma, of also eightstacked Ophiuchus comes the — sample. disproportionately cluster. and than that Centaurus The Asmagnetic — signal the fields, is from central an the also enhanced regionsthe sample notably signal of DM of from stronger cool local central than bright core cool for galaxy core the regions clusters is full host a particularly natural high prediction of of reversals among spiral— arms). and indeed The required above by puzzling — this features model. are therefore consistent with of the galactic centrethis and review region. models forgalactic In the centre. section4 magnetic fieldswe Inof and study section5 galaxies free thewe optimised electron for consider density phenomenology in the observations of DM of ALP-photon other conversion galaxies in and the provide a list JCAP04(2015)013 for (2.5) (2.2) (2.3) (2.4) (2.1) ψ m . yv 2 θ √ = given by θ νγ → ψ . l, d . At the one-loop level, 1 keV, it would predom- ) . = 0 ~ B, ¯ νν · ν   = 7 ψ ~ E z y l, %, φ , ψ a a γ ( → γ m with the decay rate, 5 ψ m   ψ ν m aγγ DM 5 g ρ 2 F γ ) are cylindrical coordinates within   . µ x G s , ≡ . ) o i∂ . θ %, φ ¯ 3 ψ 2 is the Fermi constant, sin l ψγ ~ with the decay rate Γ B Z Λ a − (2 m · F µ Λ 2 φ ∂ π G ~ νγ   d E 1 sin a % 16 a → 4 d γaz 1 γay M π ∆ = if Λ is independent of the mixing angle % – 4 – ψ ∆ ∆ EM ≡ α νa νγ γ 9 F -direction in the presence of a classical background FOV → 1024 -mediated channel → γaz µν x Z ∆ ψ ∆ ψ Z ˜ ∆ F Γ = νγ µν γ F π νγ → γay 4 ψ ∆ ∆ → aF . Since then the 3.5 keV signal has also been interpreted in ∆ Γ ψ 11 Γ 1 M   = − 8 + 10 νγ 1 the angular radial coordinate. → × ω L ⊃ ψ % 7   F is the ALP photon coupling. The linearised equations of motion for a 2. The total observable photon flux in the field of view is then given by ≈ propagating in the 1 √ is the fine-structure constant, ) , are given by, [20] − θ ω v/ ~ B 1 (2 M 137 2 = ' γ denotes the interaction which induces Faraday rotation between photon polarisation is the distance along the line of sight and ( → EM aγγ F g l α a In the presence of magnetic fields, ALPs may convert into photons in a process akin to If such a sterile neutrino constitutes dark matter with Reference [1] showed that, if the unidentified 3.5 keV line is interpreted as arising from The scenario of [10] considered in this paper is however crucially different from these Here ∆ states in an external magneticALP-photon field. conversion, we As will we will neglect be these concerned terms with in the the total subsequent photon analysis. flux from that of neutrino oscillations.ALP line As may we produce will an associated now 3.5 discuss2.2 keV in photon more line. detail, in this way a 3.5 keV where which is in principle independent of Γ The relevant interaction term for axion-photon conversion is the Lagrangian operator, where mode of energy magnetic field, decaying sterile neutrinos, thenvanishing, sin the mixing angle is determined to be very small but non- models in that thean otherwise photon ‘invisible’ line ALP is line.both a Decay fermionic secondary, modes and environmental for scalar effect darkto dark due matter an matter particles to ALP into [10]. and the ALPs a existence For exist neutrino example, for of through fermionic the dark operator matter can decay inantly decay through thecharged ‘invisible’ currents induce the decay channel where the Higgs VEV the field of view, with a variety of modelsemission in of which dark a matterparticle photon. decays, have been annihilates Among considered or these, in de-excites [14–19]. models with the involving prompt axion or ALPs as the dark matter JCAP04(2015)013 = pl (2.9) (2.7) (2.8) (2.6) ω (2.10) scenario, scenario. γ γ → , where → l, ω 2 as a 2 a . / ) d L/ → 2 2 pl → = ω L/ , = − x l, %, φ x i

( i | = dl , γ . 2 ) γ | 2 to → l z ( a !#   γ P | DM x L/ ) ) ) ) DM x x − m )d + ( ( x ρ x ( 2 = ( | a (in this work we assume vanishing y ∞ γaz γay GC x l, %, φ DM γ l M ( | Z m 2 2 /ω ) ∆ 2 a ) ∆ DM L/ x = L/ ρ ( x − m FOV 2 ( . i Z s γ the free electron density. The axion-photon − i| . γ i γaz o f . e l | → = − n a 0 Z , ) ∆ P a – 5 – φ scenario ) 0 ∆ 1 1 h x d , ( x γ ( 0 % 0 ∆ γ DM |h d iωL γay FOV ∆ propagating from % → − πτ + ∆ Ω 2 4 2

a denotes the magnetic ﬁeld in the directions perpendicular   i| L/ i FOV ' f − Z | → B exp γ = 0 ) = a " x , →

x a x → 0 ( π T , T → ) 4 1 DM M = |h , a Γ DM , where i z -ordering’ operator. For an initially pure ALP state, the ALP-photon = photons would vary from cluster to cluster in a DM F f x = | M , γ γ 2 y → / γ → νγ i denotes the average conversion probability over the telescope field of view, a → B P ψ = ( is the plasma frequency with = 0). Formally, we may write the general solution to equation (2.5) for an = i F 2 FOV i a / | i 1 γ m ) γai e → denotes the ‘ a P x /m h is the angular size of the field of view in steradians, and the dark matter density is e T The refractive index for photons in a plasma is given by ∆ παn FOV ALP mass initial state, As we will discussefficiently in in section4, the ALP-photon very conversion centralflux in region is the close then the to well-approximated Milky Sgr by, Way A*, only if proceeds at all, and the observable photon line where averaged over the field of view. 2.3 Predictions of the DM with shorter decay times beingfields. inferred Within for clusters a withmagnetic cluster, stronger field the or line strength, more strength in coherentThe magnetic should particularly central region approximately peaking of trace strongly coolof out in core the non-cool clusters the square will core centre also ofReference of clusters. give the [13] a cool also stronger These core noted signal predictions clusters. that, than the due were central to further region the discussed increase in and magnetic quantified field in strength at [13]. the centre of Ω (4 to the ALP direction of travel. Finally, ∆ Here, conversion is then given by, In this scenario, thecoherence strength of the of magnetic theThe field, photon total and line predicted the photon then dark flux depends matter is column on then density both given along by: the the magnitude line of and sight. Here we briefly review predictions made in previous work for the DM mixing induced by theelements ∆ Lagrangian operator of equation (2.4) is determined by the matrix where With regards to galaxytime clusters, assuming reference DM [10] showed that the would-be dark matter decay JCAP04(2015)013 . 0 × 5 . 55 keV . 3 F conversion. ∼ γ corresponds to E → 0 a , consisting of 4 CCD 0 8 . by 16 0 8 . , which equates to an upper limit of – 6 – 1 − 1 s 2 − erg cm model. ALP to photon conversion in the bulk of the Milky γ 14 − → 10 a × . The baseline fitted background model also included atomic lines → 3 1 − s . 2 − F As it plays an important subsequent role, we first review details of the XMM-Newton With regards to galaxies, reference [12] found that the conversion probability in the In the Chandra observations of [3], a 95% bound on line emission at As the uncertainty in the background modelling is large, it is possible that the assigned photons cm 6 We thank Signe Riemer-Sørensen for communicating these to us. 1 − Way has been studiedthe in photon flux. [12] and However,section before found3.1 discussing tothe the be predictions importantwe of too aspects review this inefficient of the model, to themagnetic we pertinent contribute field observations first aspects significantly in review [3–5] the in to of in central some the region detail. observational of the models3.1 In Milky for3.2 Way. theand Observational3.3 , electron searches density forThe dynamic the and centre 3.5 of keV thesource line Milky Sgr Way A*. from is the We the take galactic supermassive a black centre distance hole of associated 8.5 to kpc the to radio the galactic centre, and so 1 and Chandra telescopes. The archivalACIS-I Chandra configuration observations analysed which in has [3] a involve data square from field of view of 16 Reference] [12 also predictedthe a centre sharp of decrease M31,line in as the of the signal sight. magnetic strength fieldmuch Furthermore, as weaker (following than [12] we the in move predicts a spiral away galaxyspirals that arms) from cluster. will the becomes give Reference the 3.5 parallel [10] strongest predictedthe keV to line that, disk. the line signal, among as signal galaxies, the edge-on in ALP will a propagate typical a larger galaxy distance is through 3 The Milky WayMotivated centre by recent analyseswe here of determine X-rayachievable line the in emission circumstances the under from DM which the a Milky signal Way centre from in the [3–5], Milky Way centre is 2.47 pc at the galactic centre. Milky Way halo is tooin M31 low is to much produce higher, with an M31 observable displaying signal, highly beneficial while conditions the for conversion probability a cluster, the would-bebe decay greater time than inferred the fromfits decay local in time clusters the inferred that field from of fill more view. the distant field clusters, of where view the will entire cluster chips I0–I3. TheXMM-MOS archival XMM-Newton or observations XMM-PN analysed cameras.of in These the [4,5] involve are chips, slightly with different but either geometric in the arrangements both cases result in a fieldwas of derived view as with approximate radius of 15 Observations with MOS1 after(two) 2005 CCDs (2012) following have micrometeorite reduced damage. coverage due to the failure of one line strengths may hidethat an as actual they do dark not matter come signal. with error A bars caution (due on to these difficulties line of strengths making XSPEC is converge) it 10 from K XVIII atthe 3.48 line keV, flux 3.52 isline keV sensitive strengths and for to an the the base Ar strengths fit line assigned to at to the 3.62 these data. keV, lines. and In the table1, upper we bound collect on the JCAP04(2015)013 ) ) 1 2 1 2 − − s 8 . For the MOS s 2 − 2 8 2 − 9 8 8 − − 10 8 8 − − − − − cm 10 2 × cm . 10 10 10 2 2 10 10 2 × − 9) − × × × . 1 × × . 0 2 8 8 2 . . . 7 3 . . 9 1 1 ± 7 5 . 5 . (5 Strength per arcmin Strength per arcmin (ph arcmin (ph arcmin ) 5 1 6 6 6 6 − − − ) − − − s 1 10 5 5 2 10 − 10 10 10 − − − s × × 2 × × × 10 10 − 5 5) 2 2 2 . . . . Strength × × 0 2 4 4 . radius around Sgr A* is masked. Hence, for the – 7 – 1 8 (ph cm . . 0 Strength ± 4 2 5 . 9 (ph cm . (2 3.48 3.52 3.62 (keV) Energy 3.55 keV 3.5 3.5 3.53 (keV) Energy . In [3], the central 2 2 Element Ar XVII K XVIII K XVIII Detector XMM [5] XMM-Newton observations of the galactic centre region: line emission detected XMM PN [4] XMM MOS [4] 95 % Upper bound Observations of the galactic centre region with Chandra [3]. We give the 95 % upper bound 5 keV with high significance. The former paper however focuses on interpreting this . 3 Using archival XMM-Newton data, references [4] and5] [ both detect an emission line at The line strength observed with XMM-Newton is at a level markedly stronger than the The above results all come from relatively recent papers. It is possible that once these There is further reduction in field of view due to masking of point sources, corresponding to an additional 2 ∼ 7% reduction [3]. Wewe omit do this not here know as the a similar percentage point of source field masking of was view carried lost out there. for XMM-Newton, Given and the other uncertainties, this error is minor. E line in terms ofinterpretation. K XVIII The emission fluxestreated while the as the effective observed field latter of by paper view focuses XMM-Newton of on the are MOS a shown and possible PN in dark chips table2. as matter 530 arcminute We have upper bound from Chandra observations.it In is terms of unclear interpretations what involvingand K importance multiphase, XVIII to lines, and place itof on is view this: involve conceivable a that theHowever, higher the this galactic average would regions centre K be environment enclosed abundance surprising is by than for complex the those the within XMM-Newton case theanalyses of field Chandra are dark field matter refined decaying of andfluxes to view. checked, from produce and XMM-Newton photons. any and systematicabove Chandra differences results will accounted cannot be for, be consistent the taken with 3.5 as each keV the other. final In word any on case, the the matter. In studying the morphology Table 2. camera, this comes fromthe averaging appendix the of field [5], of and view we of have MOS1 assumed and the same MOS2 field from of the view tables for in the PN camera. around 3.5 keV. is possible that thereFor is subsequent actually comparison no with statistically XMM-Newton significantflux observations, line per we emission re-express arcminute at these these in frequencies. terms of Table 1. on line emission andvalues also are fitted not values for necessarily atomic statistically lines distinct included from in zero). XSPEC [21] (note that these fitted analysis in section4, we use an effective field of view of 240 arcminute JCAP04(2015)013 is ) = y (3.1) r, b, l ) coordi- scenario, γ , = 10 pc and → x, y, z 2 a ) GC y GC → 2 z GC H − This electron density is z ( 3 − scenario, we aim to provide 05) [22]. This corresponds to γ . 0 exp → − , a 2 ) 06 . → 0 GC y − − 2 GC y L ) = ( + ( l, b 2 – 8 – x − exp points vertically upwards out of the galactic plane (to- 3 z − = 0. Also note in the NE2001 model, the electron density z = 26 pc. This dominates over thin and thick disk components 0) corresponds to the centre of galactic coordinates ( 4 pc). and , . 0 7 = l (100) pc from Sgr A*, while our interest is only in lines of sight , GC − y O , H ) = 10 cm = -coordinate points from the Milky Way centre towards the sun, 9 pc x x . x, y, z ( ). However note that, in these coordinates, the true dynamic marker of the b ) = (8 GC scenario. e, γ n 0). The = 145 pc and , 20 pc. However, note that the physical offset from Sgr A* is reduced as Sgr A* SgrA* 0 → , − , z GC a L Let us enumerate the caveats on the above electron density. We first describe the coordinates used. We use right-handed Cartesian ( In this paper, we will use the NE2001 model for the Milky Way electron density [23]. The One aim of this paper is to explain how, in the context of the DM = → More detailed studies of gas distributions within the inner 10 pc appear in [25]. 5 kpc 3 . SgrA* GC y derived via pulsar dispersion and emissiondensities measures, along which are the sensitive line toand integrated of does electron sight. not account The for electroninterspersed patchiness, density or by the thus voids. presence determined of It isall dense a is clouds lines with smooth also partial of function, a filling sight factors single within simple function that will represent a fit to data for z in (3.1) is formallyHowever, truncated this truncation to reflects zero anthe when abrupt galactic the change center, argument in and of scatteringrather can the diameters be than for exponential omitted its OH is if masersuse less fluctuations we in (3.1) than (see are as -1. interested our the only baselinecomponent discussion electron in of density in the [23], model free which section inof becomes electron 2.4 this our comparable density paper. region of to of We the [24]). also interest. galactic include centre the We component thick shall at disk therefore the edge is itself offset from in the innermost galaxy. The centroid of the distribution is offset by with these differences in XMM-Newton andanalyses Chandra - fluxes - can which arise mayplane, or naturally. and may not In so survive thisplane, future the scenario, contains XMM-Newton the more field signal signalthe of is region. galactic view, suppressed centre. To within which understand the extends this galactic further we vertically3.2 now out discuss of the the Electron astrophysics density of As discussed in section with2.2, ALP large to electron photonin densities conversion the depends suppressing Milky on the theDM Way conversion free centre electron amplitude. is density, therefore The an electron importantnates, density input where into the the origin(8 resulting (0 signal forin the direction of decreasing NE2001 model contains severalthat components, is and given in in our particular notation a by, galactic centre component wards positive Milky Way centre Sgris A* slightly (where offset, the with majority a of physical location observations considered of ( here are centred) of the 3.5 keVdistinct line predictions from for the this galactic scenario centre that in can the be DM tested more precisely in future studies. ( JCAP04(2015)013 conversion probability. γ → G) within the galactic centre a 1 mG inside, but no such large µ ∼ 10 B ∼ B – 9 – 8 mG. However, as the physics extremely close to 1 mG field strength. This leads to a picture of a ∼ B > G averaged over a 400 pc region, with a preferred average B µ 50 ∼ B mG [41, ],42 with such fields being produced by shearing of the poloidal ∼ G over the entire galactic centre region. µ B G[40]. However, Faraday rotation only probes the component of the magnetic µ 100 10 ∼ ∼ B B Magnetic field estimates have also be reported for smaller sub-regions within the central Faraday rotation measurements generally prefer low values for the central magnetic In contrast, a much lower estimate is suggested in reference [30], which argues for a In [37], the spectrum of synchrotron emission from the galactic centre was used to obtain There exists a longstanding case that the magnetic field within the galactic centre is 150 parsec. Dense molecular clouds are widely argued to support horizontal magnetic fields 150 parsecs [33–36]. This argument arises from the presence of nonthermal radio filaments the supermassive black hole can be expected to differ substantially from that of more distant ∼ of the order of field along the line ofto sight, the while line ALP of tothat sight. photon there For conversion a are relies field significant onFaraday with the reasons rotation random field to orientation, estimates perpendicular think these of thatmeasurement will of the the be the galactic comparable, parallel strength but centre magnetic of given field field the is transverse cannot strongly field. be poloidal, said to give a reliable field by cloud motionsreference or [43] tidal found a forces. magnetic At field a distance of 0.1 pc from the central black hole, field, field outside. The fieldperhaps in enhanced the by filaments compression is but is regarded not as representative a of local the and wider dynamical galactic feature, centre field. that is relatively weak pervasiveregion. poloidal These magnetic lower field magneticon ( field studies estimates of are shortradio based filaments pc-scale on are equipartition nonthermal localised arguments radio dynamical [38] filaments structures and [39]. with On this view, the large-scale field of a minimal magnetic field of pervasive milligauss field, locally illuminated by injection of relativistic electrons. dominantly poloidal (vertical) and with∼ a uniform milligauss strengthin throughout the the central galactic centreemitting region, via orientated predominantly synchrotron orthogonal radiation.even to though the These galactic some filaments planethe are are and clearly filaments remarkably against interacting straightpressure, with collisions and molecular leading with uniform, to clouds. molecular estimates clouds The of can apparent a be rigidity used of to infer their magnetic Unfortunately, the magneticknown, field and estimates in vary by thein two orders this central of region 100–200 magnitude. arisesfrom pc As from the the different of galactic Milky processes centre the Way tobrief magnetic magnetic Milky field the summary field bulk of Way model of the ishigh of the observational to poorly [26, galaxy, possibilities low27]. this values. for area Following the is [28–32], galactic excluded we centre here magnetic provide field, a from enclosed by the fields37 of pc from view Sgr offields. A*), XMM-Newton and and in For particular Chandra alland the (extending these regions captures to caveats, along genuine them a the features withaware maximum of distribution of large of the in transverse its free magnetic limitations, [23] electron we is distribution shall nonetheless therefore in observationally use the3.3 derived it galactic in centre. our While Magnetic subsequent field studies. The magnitude, directioncentre and region coherence are clearly of important the for transverse us magnetic to field determine in the the galactic JCAP04(2015)013 (4.4) (4.2) (4.3) (4.1) dependence of the (local dark matter 2 3 B kpc /

conversion probability scales M , 6 dl . γ 2 10 − , DM → DM × 2 ρ cm m ) a 4 s . 28 ∞ GC s l r/r r 10 Z s z , = 20 ρ × s As the 2 ρ FOV (1 + . i 4 2 r γ 150 pc along sight lines within the XMM Newton – 10 – ' → = 1 mG ˆ a < ) = P dl ~ | r B h ( is just achievable. Due to the x | DM DM γ DM ρ 1 m for NFW πτ → ρ at the centre of the Milky Way z 4 ∞ ]. Averaging over the full XMM-Newton field of view, the GC l a 1 keV. γ Z ' . ? → sr → 5 kpc and outwards. = 7 F . = 1 mG ˆ a 150 pc in the galactic plane, with the electron density as given by ~ DM B 8 kpc [ = 8 . . scenario. → m γ GC r l = 10 → s a r → is the distance to the galactic centre, , this maximises the resulting signal. We will see that in this maximal scenario, an 2 r B The photon flux is sensitive to the dark matter column density. We use an NFW It is clear from the above differences that no definitive statements can be made about the In this paper, we will primarily focus on the first, maximal, scenario involving a poloidal The predicted photon flux per unit steradian is then given by (2.10), We note that magnetic flux conservation implies that the strength of such a field cannot fall off rapidly 4 where we have used on a scale of 20–40 pc above the galactic plane. profile [44], given by As sufficiently large conversioncentre, probabilities are dark only matter obtainedsignificantly in decaying to the between the vicinity observed Earth ofgalactic photon the and centre flux. galactic at the Consequently, the galactic integration centre in does (4.4) is not from contribute the where galactic centre magnetic field,different and it estimates is and farand measurements. beyond radio the Further continum, scope studies as ofand well this of Zeeman paper as Faraday splitting to improvements rotation willcentre in reconcile help measurements region. these the to far get infrared/submillimiter a clearer polarimetry picture formagnetic the field magnetic field with in milligauss the field galactic strength. regions, it isfrom unclear Sgr A*. what this implies for the magnetic field at distances of 10–100 pc density) and column density is given by, with observable signal from DM signal, it follows thatdetail: we they do are not incapablein need the of to DM generating consider an the observable other 3.5 (medium keV and line low) from scenarios the in galactic centre We are now ready tothe discuss Milky the Way. We characteristics use of the ALP maximal to model photon for conversion the in magnetic field the discussed centre in of section 3.3, i.e., 4 Dark matter in the central for the galactic centreparticular, and we assume thick disk components of the NE2001 model, cf. section 3.2. In and Chandra field of views. JCAP04(2015)013 GC (4.7) (4.8) (4.9) (4.6) (4.5) /L i x . ) 0 x , ( e . n 0 . ) 0 2 , dx x − ( 2 1 ω

x 2 2 pl ) 5 keV x . cm ω . This suggests that a pertur- x 0 Z 3 3 ( e a − 28 i dx γ πα 2 , 10 2 ∆ ωm L/ ) x i × x GC − x ( 9 Z . L GeV iϕ 2 = 10 cm M 1 cos π ω 2 13 e 2 − √ − n dx e 10 dx 27 2 2 ≈ -integral to obtain an argument of the cosine 2 0 2 ) = 10 L/ L/ x 0 L/ − L/ – 11 – x × − ( Z i

Z γ GC 5 ⊥ x . 1 L ∆ 3 B z,y 0 1 mG = dx X i ' dx is defined as in equation (3.1). For the maximal magnetic 2 2 2 dl Erf L/ × L/ = 0 and taken ) = L/ GC − x 3 a − L Z L DM − DM ( Z 2 ρ γ m 2 10 ⊥ → and propagating through the galactic centre region of the Milky M B a ∞ ) = ≈ 4 GC γ l P x Z ( ∆ ω 2 eff ϕ ⊥ ) = 2 may convert into a photon with the probability L B ( 2 a Mm γ L/ → = a P x 2, respectively, where 2 to , L/ Other models of the dark matter density can result in quite different column densities: The strength of the ALP-photon mixing can be estimated by considering the ratio, = 1 − i = field model of equationthe (4.1), central region we of take the thethat Milky magnetic the Way, and field leading for to order thefunction be purpose Taylor over expansion of approximately the an of constant relevant analytical interval. the over estimate, Explicitly, error we we expect functions approximate, should well approximate the For a constant magnetic field, this expression may be further simplified to, For an electron densitythe with a NE2001 Gaussian model fall-off —which — is we such proportional may as perform to thefor the the galactic difference centre between component two of error functions with arguments bative, small mixing approximationto of the the full interaction solution. shouldx provide To linear a order, good we approximation find that an initially pure ALP state travelling from for the 10 profilescolumn presented densities in are the in appendix the of range [5] (7 NFW, Einasto, ISO and BURK), the where we have specialised to ∆ where, This uncertainty should be kept in mind when flux values (4.2)4.1 are calculated in the ALP following. toWe photon now solve conversion equation probability (2.5) tonegligible derive mass, the ∆ axion-photon conversionWay. probability for We ALPs will with dothat this a in two small-mixing ways:equation perturbative (2.5) first, approximation numerically we is by will discretising appropriate, solve the equation and evolution (2.6) of second, analytically an we by initially will noting pure ALP-state. solve JCAP04(2015)013 . ! (4.10) 2 ) GC 2 GC z H − z ( + ) according to a 2 ) y, z GC 2 GC y ). This explains the L 2 − y ( M (4 − e / 2 L L e 2 ⊥ (0) e B ωm παn 30 pc. ) =

L & 2 ( GeV. z γ sin → 13 -axis). As observations are centred on Sgr A* a y P 2 ) = 10 GC 2 GC z H − – 12 – M z GeV. The outer solid circle indicates the field of view ( + 13 2 ) 0). GC 2 GC = 10 orientation to , y L − ◦ y ( M = 300 pc, 2 L ) = (0 as a function of the galactocentric coordinates ( e γ 2 ) y, z → a (0) e 2 e P n ( m 2 2 ω M 2 ⊥ 2 B α 2 π 4 The values of ) = L ( γ Figure1 shows a marked suppression of the conversion probabilities at low values of -axis) and the dashed square (45 → y a . This arises as the conversion probability is sensitive to the difference between the ALP P apparent constancy of the conversion probability at z mass and theelectron plasma densities frequency lead to - aphoton and large conversion the ALP-photon probabilities. mass latter differenceand At is the and resulting larger a set ALP-photon galactic suppression conversion by probability ofexpansion altitudes, is the the of well the approximated ALP- the free by electron cosine the electron zeroth in density order equation density. is (4.8), lowest giving High This conversion probabilitywhich agrees we well show in with figure1 thatfor obtained from a numerical simulations, Figure 1. numerical simulation of (2.5) with where the subleading correctionsimation, appear we at may cubic perform orderprobability, the of integrals the of argument. equation With (4.8) this explicitly approx- to obtain the conversion of XMM-Newton. Theto field of view ofthey Chandra are is slightly indicated offset by from the ( solid square (parallel orientation JCAP04(2015)013 , . i 2 were ) 0 GC 2 GC z thick disc e H − n z coordinate ( z . In deriving to obtain the + 2 ) . Note that the 0 and 8 GC . 2 GC y y L − thick disc e 16 in the central region, y n thick disc e ( 150 pc within the field )-plane, and these are 3 × n + 0 − < 8 + − y, z . , the argument of the co- | e h GC e x | n n GC e 1 cm and not that from . n exp 20 pc region where the electron = e = (0) e GC e (although only the inner 14 = 0 n n n e 0 z > . According to this model for the n x scenario are now easily obtained by ) = γ and thick disc e → , y, z z n (0 a GC → e, – 13 – n , this ‘small angle’ approximation is in good agree- 3 − . ◦ = 1 mG which is constant for 1 cm . 0 ⊥ = 45 B r ≤ α e n , of Chandra was not fixed during the observations considered in [3], r α , which explains the suppression of the conversion probability near the in our notation, most of the region with high conversion probability falls . For 2 2 ◦ )) M 4 = 0 / , y, z r 2 for the actual XMM-Newton field of view for the observations in [4,5]and 240 α L (0 2 2 ⊥ for the actual Chandra field of view for the observations [3]. GC B (eff) e, 2 = The field of view of the XMM-Newton observations of the galactic centre is a factor We note that while the galactic centre contribution to the electron density dominates At lower galactic altitude, the factor The roll-angle, 2 times larger than that of the Chandra observations. Furthermore, as the XMM- /n γ . → a Newton observations include a substantial coveragedensity of is the suppressed withprobability respect for to XMM-Newton that is of largerview. the than For galactic that a plane, of magnetic Chandra the field when ALP-photon of averaged conversion over the field of of 2 electron density, the thickand disc our contributes full with modelequation of (4.10), the electron we density only should included then the be contribution from used in [5]), while Chandra has a square total field of view of 16 outside the field of view.the tilted A slightly field larger of average view conversion with probability can be expected for in the verydisc’ centre component of of the the galaxy, NE2001 it model quickly at drops large below the contribution from the ‘thick that encodes thejustify effective a line-of-sight zeroth electronare order the density expansion. spatial fordirectly oscillations a On sourced in by given the the the path, varyingapproximation, contrary, conversion line-of-sight4.10). ( the probability is electron densities, in most In too as addition, the strikingof is large the ( clear (1 feature to from conversion of the probabilitygalactic analytical scales1 figure plane. with an overall factor This neglect however, is harmless: for small enough valuesment of with the numericalof equation solution (2.5) of with equationresults the in (2.5). full sections NE20014.2, We electron 4.3 used density and5. a full discretized simulation 4.2 Predictions for XMM-NewtonThe and predictions Chandra fromcombining the (4.2) dark matter andconversion DM the probabilities simulation in resultsNewton the has of total a radial field2.5). ( total of field view of We view of first with XMM-Newton a compare radius and the of Chandra. 15 ALP-photon XMM- axes, hence and hence the exactmay orientation well of have the varied.is detectors As sensitive during the to each average the observation conversion orientation,the was probability we symmetry not over here axes the fixed of consider the Chandra two and Chandra extreme field field cases of of as view view indicated are in aligned figure1. parallel to If the arcmin sine of equationP (4.8) can be Taylor expanded with the leading order contribution giving searches for a 3.5total keV line one in for the both530 galactic XMM-Newton centre arcmin actually use [5] a and smaller Chandra field [ 3]. of view As than discussed the in section 3.1 , we use JCAP04(2015)013 (4.11) (4.12) (4.13) (4.14) (4.15) here has GeV were 5 2 13 M DM = 10 τ scenario. M . 60 is highly sensitive γ ◦ ∼ ◦ → . Even within Coma, the a , , s and 3 . = 0 = 45 2 2 − 2 24 → − − r r − α α . 10 DM, GC cm cm cm ◦ 1 1 × /τ 1 ◦ − − − GeV in the stacked cluster sample. = 5 13 = 0 = 45 1 for 0 for . . r r clusters , α α DM τ = 2 = 2 = 10 DM 80% reduction in the field of view. This s would make the prediction in [12] of no observable τ 5 5 5 5 photons s photons s photons s 24 − − − − M ∼ 5 6 5 10 10 10 10 10 6 for 4 for − − . . − × for 4 4 – 14 – × × × × 10 10 3 10 20 pc, see1. figure The field of view shrinks from ( 4 5 0 0 − . . . . × × × 1 1 3 3 = 9 7 10 1 . . z > .        ∼ = = 2 = 6 = 2 XMM Chandra F to estimate the Chandra flux. The value of model can reconcile the conflicting results from Chandra and GeV, we find an expected photon flux of, F 20pc ◦ XMM γ XMM , but since the field of view averaged conversion probability is 13 z> i XMM Chandra F 2 Chandra i γ F → γ F → = 45 a a → = 10 a r P h P α → h M comes from numerical simulations of the centre of the Coma cluster in [46]. s, by an order of magnitude from 5 3 − 22 DM to 90 arcmin τ 10 2 × , the observations of a 3.5 keV line from clusters and from the galactic centre may 2 0 . conversion probability region M 4 For comparison, in [10], the parameter values Finally, let us apply a masking that restricts the field of view of XMM-Newton to the 20 pc region is masked out, despite the − = 8 DM Decreasing τ 5 10 DM prediction is easily testabledark and, matter if model. confirmed, would be difficult to explain within any other XMM-Newton if the magneticpredict field that in the thez clear galactic > majority centre of is large the enough. XMM-Newton signal In will addition, remain we when all but the been set to match the XMM flux observedused, by motivated [5]. by the observedto flux photon from conversion galaxy probability clusters of [1] and an estimated average ALP 530 arcmin significantly larger than for theto total field (4.13): of view of XMM-Newton, the flux isWe rather see similar that the DM ∼ both be explainable as originating from dark matter in the DM This value of 10 magnetic field is uncertain toconversion a probability. factor It of two, isbright corresponding cluster also to Coma probable a are that biased factorWe high of conversion shall compared four probabilities to also uncertainty those in in see for the into a centre stacked section the average 4.3 of assumed ofthat many electron the clusters. for this density small ratio profile changes of in in the thein electron galactic scale centre, height. and Therefore, can despite vary the by large a apparent difference factor of 10 There are however significant uncertainties on this number of 10 signal in the MilkyWay Way slightly halo less to strong, two but (instead only of by three) changing orders the of predicted signal magnitude from weaker the than general that Milky from galaxy clusters. of view, the ratio of the averaged conversion probabilities is given by Combining the larger conversionwe probability find that of the XMM-Newton expected with photon flux its ratio larger between field XMM-Newton and of Chandra view, is given by, Such a substantiala flux non-detection ratio in isτ Chandra. consistent with For a the detectable dark signal matter in column XMM-Newton, density and given in (4.4), and for where we have used JCAP04(2015)013 where the z GeV. Right: the ratio GeV. Right: the ratio 13 13 = 10 = 10 M M -direction. Here (2–5). This corresponds to a line flux ratio z O ) for XMM-Newton (blue) and Chandra (red) as a ) for XMM-Newton (blue) and Chandra (red) as a – 15 – i i γ γ → → a a P P h h ( ( 6 pc. 10 10 . of the electron density. Here 12 − smaller than the default value of 26 pc, more of the field of GC = = 26 pc. H ∗ GC as a function of the scale height. The vertical dashed line indicates the as a function of the off-set. The vertical dashed line indicates the default GC H (4–11). SgrA H z − ∼ O Chandra Chandra i i with smaller electron densities and thus higher conversion probabilities. γ γ GC z → → z a a P P Left: the values of log Left: the values of log h h Chandra / / F / XMM XMM i i The dependence of the averaged conversion probabilities on the off-set of the elec- For a scale height γ γ XMM → → F a a P P h default NE2001 value of tron density aregions shown at in figure2. high Regardless of the off-set, XMM-Newton captures re- function of the off-seth of the electron density in the function of the scale height 4.3 Sensitivity toIn model section parameters 4.2 we notedtains that a for the higher defaultelectron averaged model density conversion of is probability the suppressed.set electron by The density, of significance XMM-Newton observing the ob- of regions electron thisof density at effect which from appear is large the in highlyvertical galactic [23] dependent offset without centre on of error and the the bars. off- the50% electron Here, vertical from density we scale their by consider height, 100%, default the the and values. effects deviations values of of deviations the of vertical the scale height by The ratio ofviews conversion for XMM-Newton probabilitiesof and — Chandra after — is averaging over theviews corresponding of both field XMM-Newton of and Chandra capture low electron density regions. This leads NE2001 value of Figure 2. Figure 3. JCAP04(2015)013 plane corre- (4.16) (4.17) y . While - G 2 scenario, x γ M DM cylinders with → τ a rf N → , are also factors of the ◦ ◦ with GC , , G L 2 2 = 0 = 45 − − r r α α cm cm 1 1 − − 1 for 0 for . . (1) factor has a negligible effect on the = 2 = 2 O = 100 pc with magnetic field 1 m 7 7 7 7 photons s photons s − − − − z 7 8 10 10 10 10 − − . – 16 – × × × × 10 10 γ 0 4 5 0 . . . . × × → 3 1 1 3 9 7 . . a        100 pc to (1–6). We note that the predicted conversion probability to calculate the Chandra flux. As expected, these fluxes − = → O = 2 = 6 ◦ = z = 45 XMM XMM r F i Chandra Chandra α i γ F γ → a → a P h P h -direction and the in-plane suppression length y As mentioned above, only the uppermost end of the observational estimates for the In [9], stacked Chandra and XMM-Newton observations of galaxies were used to con- with gridlength 3 pc overthis a magnetic disk field with model radius are 50 pc. The averaged conversion probabilities for galactic centre field leadlowing to magnetic an field obervable model: signal. an To ambient quantify magnetic this, field we of also 0.1 consider m the fol- conversion probabilities. 5 Searching for theIn 3.5 this section, keV we discuss line theWay search in and for the the other 3.5 inferred keV galaxies constraints X-raystudies line on in of dark galaxies matter other the than models. the X-ray Milky We line argue that in currently other published galaxies are consistent with the DM the off-set in the electron density, a variation of their values by an radius 0.5 pc stretchingsponding from to observed radio filaments. We organize the cylinders on a grid in the are a factor of 100the lower than magnetic in field the strength casecontribute of by to a a the pervasive conversion 1 factorcentre mG probability. of field, cannot In 10. corresponding be this to explained field The reducing by model, radio DM the filaments signal are from much the too Milky narrow Way to strain the proposed sterilespectively, archived neutrino data origin from ofMs a the and sample line. of 14.6 81 Forlines Ms and Chandra from was 89 and decaying considered. galaxies XMM-Newton dark with re- The matter a stacking total by exposure was minimising of made the 15.0 so X-ray as background. to To optimise avoid sensitivity an to ICM to higher averaged conversion probabilities, asprobabilities is are evident again from in3. figure the The range is ratio substantially of conversion increased byin small the increases scale in height. the This electron would correspond density to offset a or much lower small predicted decreases value of while the predicted fluxes become where again we have used and we also provide asignificant list exposures of for which target a galaxies detection in of the the XMM-Newton 3.55.1 and keV signal Chandra is archives more with Observational likely in hints thisThe and scenario. first constraints search forcombined the XMM-Newton 3.5 spectrum keV line ofsection1. in the a central galaxy region was of that M31. of [2], We who reviewed detected this the result line in in the JCAP04(2015)013 σ 2 keV . 6 Ms of ], where . 4–6 . vir ,R . vir R 01 . , no detectable signal 1 keV were included γ [0 & → ∈ T a r → 2 keV for Chandra and 2 . 6–5 for the Chandra spectrum and at 11.8 . σ scenario depends on the magnetic field along the model in other galaxies – 17 – γ γ → → a a → → depending on assumptions. σ or 4.6 σ denotes the estimated virial radius of each galaxy. The resulting X-ray spectra were While the origin of galactic magnetic fields is not well known, enhancement of small In [8], a search for the 3.5 keV line in stacked XMM-Newton data from 0 These results of [8,9] provide strong constraints on scenarios with dark matter decaying . 100 pc (the typcial size of a supernova outflow). The random field may be enhanced to vir G strengths by turbulence within the galaxy. Many spiral galaxies also have a regular R then argued to be dominatedlines, by the instrumental search background. was To then avoid restricted prominent instrumental to the ranges 2 background, no galaxies inin the clusters sample. or groupswas In with addition, only to temperature extracted avoid from emission from an the annular inner-most region regions within of galaxies, the data radius would arise for these searches. 5.2 Predictions for the DM seed magnetic fields throughdevelopment. dynamo mechanisms The providecomponents. magnetic a The plausible fields random explanation field in for∼ is galaxies a their short can scale, be tangledµ magnetic split field, with into coherencefield contributions length that from is coherent three mean-field over dynamo, large which distances. produced These spiralthrough may magnetic differential rotation. be fields coherent generated Indeed, over the byfollows significant magnetic a the distances field pattern mechanism in of the like disc the the direction of spiral a of arms. spiral the galaxy Finally, field generally galaxieswith is may have a coherent striated over short fields, largeplasma in coherence distances, which bubbles but length. the and the their sign Striated of associated fields the random field may fields, is be or randomised generated may arise by from the the levitation random of field hot by line of sight to thedepend point on of the decay. structure The andbetween prospects strength different of of morphological observing the a types magnetic signal of from field galaxies galaxies in (for therefore galaxies, a which review, differs see strongly e.g., [47]). for the XMM-Newton spectrum.preferred When amplitude the was amplitude found ofthe to additional the be line. line consistent was with left zero, to thus favouring freely the vary,observations the model of without 8 dwarfdwarf spheroidal spheroidals does galaxies not wasclusters. emit preformed. The stacked X-rays, spectra As thebackgrounds, were the keV-range fitted and background interstellar with a models is medium narrowimprove for cleaner the of line the fit. than at astrophysical To that and 3.55 constrain3.55 instrumental of the keV keV dark was line matter from origin addedfor of both to sterile the the neutrinos, these line, Milky a the models mixing Way contributionat angle halo and of 3.3 of and a shown the possible the magnitude not dwarf inferred to in spheroidals [1] was was considered, shown to and be excluded directly to photons. We now explain how in the scenario of DM In contrast to scenarios instrength which of dark the matter X-ray decays line or in annihilates the into DM photons, the observed for XMM-Newton. Thiswhich background any was potential fitted additional byTo emission slowly constrain line varying the would smoothing presence appearadded splines, as of to above a a the localisedadded line background residual line. at spline, of 3.57 the and Whenfrom keV, fit. the the [1], a amplitude the resulting zero-width line of fit “Gaussian” was the was found component added to compared was line be to ruled was that out fixed without at to 4.4 the the central value inferred JCAP04(2015)013 (5.1) G[47]. Note µ component how- 10–15 ∼ regular . G (as in [48]) with coherence 2 ordered µ B 1 ∼ GeV M B 13 10 9 − 10 G whose strength remains constant across the × – 18 – µ 3 6 . 2 ∼ ∼ reg B γ,dSph → a scenario, we expect no line to be observable from elliptic and P γ → scenario, decaying dark matter in dwarf spheroidal galaxies will give a γ conversion — as the regular fields have the largest coherence scales and → → γ . 2 a → L 100 pc for a dSph of diameter 1 kpc, the small angle approximation gives, a → ∝ ∼ ) γ L In the DM Spiral galaxies tend to support ordered (regular and striated) fields. The ordered fields The observed strong correlation between the total radio continuum emission at cen- Dwarf spheroidal galaxies lack both ordered rotation and significant star formation, and → a ( irregular galaxies which lackmay large-scale in regular principle magnetic givestrong rise fields along to [10]. the an path of Spiral observableis an signal magnetic suppressed ALP if by fields arising the the fromelectron plasma regular dark density frequency, matter magnetic and a decay. field significant stronger As regular is signaltypical ALP-photon magnetic spiral sufficiently is conversion field. galaxies expected will This from suggests typicallyMoreover, regions contribute the edge-on with more inter-arm galaxies small to regions for the of whichfraction a photon large line of fraction than the of the the discThe arm ALPs regions. magnetic magnetic travel through field field a should directionwithin significant yield a follows a few the larger kpc directionfor signal of of paths than the further the centre face-on from spiralnot the spiral the arms. contribute field galaxies. centre to is the Therefore, conversion.on-centre generally field for observations, transverse becomes but We paths to parallel may therefore the to indeed predict line be the that of unobservable line the off-centre. sight, of whereas line sight flux and so is does much stronger for In the DM spiral arms. Spiral galaxies,surrounding like the the Milky disc. Way, may Starthese also support burst tend magnetic galaxies to fields be can in tangled support the over very halo short strong scales. magnetic fields, however, are strongest between spiral arms where typical values are timetre wavelengths and the far-infraredinfrared luminosity correlation’, of can starturbulent forming be component galaxies, interpreted and i.e., as the themation a ‘radio- star tend formation correlation to rate have between strong offields turbulent the the magnetic are field fields galaxy. observed (indeed, strength Regions in the with of highest highly turbulent high the star-forming magnetic star starburst for- galaxies). The rise to a 3.5contribution keV to ALP the line, flux butshown from no in dSphs associated [12] is photon is therefore line too from will conversion low in be for the an observable. Milky observable The Way, signal. which dominant as consistent with expectations from themagnetic known fields dynamo [47]. mechanism, Taking do a not turbulent support magnetic significant field differential rotation.significant In most cases,P it is only the regular field component that leads to ever is not believed tothe be ordered positively magnetic correlated with field,the the combining inter-arm star the regions. formation regular rate: and in spiral striated galaxies fields, is in fact strongest in length that this value includeswe the are contribution typically from only both concernedfield the with is regular the and mostly regular the tangledcoherent field. striated and regular fields, Within randomly while the magnetic oriented. spiral field arms, M31 the is magnetic unusual in that it has an unusually JCAP04(2015)013 ◦ ◦ G in (5.2) = 90 = 90 µ i i θ θ to ◦ ) and a NFW 2 = 0 i cm θ 7 − . G poloidal field with an µ = 10 e z n 14 kpc . 0 2 sech × 2 2 7 kpc) . 3 – 19 – 160 kpc − (r 3. This is due to the significant halo component of − e ∼ × . We assume an NFW dark matter distribution with 2 3 − cm 7 − 09 cm . Expected flux vs. inclination angle for an M31-like Galaxy. = 10 = 0 (face-on). Note that in this case the magnetic field model used is e e n ◦ n = 0 i Figure 4. θ radius pointed at the centre of a galaxy (so that the central 4.4 kpc of the galaxy 0 . For the Milky Way-like galaxy in figure5, the expected flux is lower primarily due to . We will refer to these models ‘Milky Way-like’ and ‘M31-like’. We assumed that i ◦ θ For the M31-like galaxy in figure4, the peak flux is expected at inclination angle To quantify this, we simulated the expected signal for hypothetical galaxies with electron For the Milky Way-like galaxy we used the recent magnetic field model by [26] with For the M31-like galaxy, based on [11] we assume a constant azimuthal field of 5 = 90 i This is anelectron adapted density version values of givenelectron the in density thin [11]. of diskparameters For component from the of [50]. Milky [23], Way-like chosen case, by we impose considering(edge-on). a the The minimum fluxgalaxy for with such ansymmetric edge-on above galaxy and isθ below over 10 the times disc, thethe and smaller flux and so for less the coherent an field. expected equivalent Furthermore, flux rotating the will galaxy be from symmetric around density and magnetic fieldangle such as those of the Milky Way and M31, observed at inclination the central 1 kpc sphere (not considered in [26]) filled in with a 5 these galaxies were locatedwith a a 15 1 Mpcare from included Earth in the and observation). observed with a circular field of view exponential vertical scale height ofthin 1 disc kpc. components We usedark of the matter [23] electron (imposing distribution density givenWay a [44] magnetic in field minumum with the includes thick value the a and of whereas parameters significant there halo given is component in no in addition evidence [ 49]. to for the such We disk athe component, note halo disk that component cut in off the at M31. below Milky a the cylindrical disk radius of withof 20 a kpc. the scale true We height assume field ofon an in 2 exponential the M31, kpc. fall outskirts, underestimating off This the but aboveangle is and field is and clearly in sufficient flux. a the to We vastly centre predict use simplifed and the the representation overestimating qualitative electron the relationship density field between inclination only increases the flux by a factor of JCAP04(2015)013 ◦ → 65 a ≥ model. → i θ γ → , and in fact ◦ a with 0 → . ◦ This table of high- = 90 i 6 θ = 90 i θ model, the masking of the γ → a → – 20 – model, figures4 and5 make it clear that we should γ → a → Expected flux vs. inclination angle for a Milky Way-like galaxy. scenario represents an attractive and testable proposal to explain the 3.5 γ → a Figure 5. → In a search for the DM In sum, stacked samples of the central regions of close to edge-on spiral galaxies provide We consider galaxies for which the sum of XMM-Newton and Chandra exposure is at least 5 ks. 6 model depends on the magnitude and the coherence of the galactic magnetic field, as well the Milky Way field.and below The the halo disc, component and of so the the Milky expected Way flux field is is not not symmetric symmetric about above the maximum flux occurs at an inclination angle somewhat above consider a stacked sample of closeNewton to edge-on and spiral galaxies. Chandra Existing archiveswe X-ray data may provide in be a the XMM- list used of to spiral perform galaxies such with a an search, apparent and diameter in of appendixA at least 1 a potentially highly interesting target for searches of signals from the DM that all have significant exposuresinclination by galaxies either contains XMM-Newton or 151with Chandra (143) total . objects raw exposures with ofof significant 7.1 targets Chandra Ms of (10.5 (XMM) Ms). reference exposures, galaxies. [9], While Furthermore, this we in table emphasise a hasfield search that some of optimised overlap our view for with would table the the differ only list γ from DM that includes used high-inclination in spiral [9].as The the strength dark of the mattergalaxy signal column from might the density fit DM within incentral the the region. field field of In of view. ourinstead view, case, For whereas focused the distant we outer galaxies, on regions onlyhigh the the of expect regular whole galaxies central an magnetic should observable fields regions.knowledge be signal should on masked the from be and If galactic the preferred. magnetic observations itbased fields However, on imply were we such that a one note observationally cannot search; that possible, decisively a rule the definitive out galaxies exclusion lack the would of with model require precise knowledge of the magnetic fields. keV line emission, assuming it is of dark matter origin. At the current time this scenario is The long total exposures ofthat such such regions in a the searchsignal XMM-Newton and depend may Chandra on be archives astrophysical suggests feasible parametersprediction with that of are the existing poorly signal data, known, strength. but thus precluding the a magnitude definite of6 the potential Conclusions The DM JCAP04(2015)013 → a of the 0 → [ks] ,[52]. XMM t This turns out to be just XMM 7 which have inclination angles n 9 8 [ks] CXO t http://leda.univ-lyon1.fr CXO – 21 – n Continued on next page denotes the number of such observations available in i θ XMM n Table 3. and of the Hyperleda database, CXO n logdc IC2560 SBb 65.6 2 65.6 1 81.9 GalaxyESO602-031IC2163 SBb Type 70.8 Sc 1 78.2 5. 2 1 40.2 1 11.7 46.4 and exposures with XMM-Newton and Chandra of at least 5 ks. These galaxies ◦ 65 In the galactic centre region, we have studied the conditions under which this scenario We have also considered samples of distant galaxies, and have further quantified the As discussed in both [4] and [5],Subsequent it to is the of appearance course of possible this that paper, the the galactic paper centre [51] line has is appeared simply claimingUsing an to the astro- disfavour function an ALP ≥ 7 8 9 scenario. In compiling this list, we only considered observations centred within 2 i the archives of Chandra and XMM-Newton , respectively. physical K XVIII line and there is noexplanation dark of matter the signal. galacticin centre clusters 3.5 keV that basedmorphology is on of compatible the the line with 3.5 morphology, keV an while line. finding ALP a explanation. 3.5 keV It morphology will be interesting to see further work on the target galaxy. Here, γ can generate a 3.5 keV line of the strength observed in [4,5]. qualitative statement in [10] thatdark matter edge-on searches spiral in galaxies thisies are scenario. with the To significant most this end archival attractive we observational galaxies have time for also in provided the a list XMM-Newton ofAcknowledgments and target Chandra galax- archives. JC thanks the Royalfunded Society by for the asupported ERC University Starting by Research CONICYT Grant Fellowship. Beca ‘Supersymmetryat Chile the JC, Breaking ‘Particle 74130061. FD, in Cosmology DM,Stephen String Portions after MR Angus, of Theory’. Planck’ Alexey are workshop this Boyarsky, at PDAJeltema, work Thorsten DESY is Bringmann, have Andrew in been Jeroen September Powell, Franse, presented discussions 2014. Carlos Stefano and Frenk, We Profumo, Tesla correspondence. thank while Signe finishing DM Riemer-Sørensen, the is paper. Oleg grateful Ruchayskiy to for Birzeit UniversityA for kind hospitality List of nearlyWe here edge-on list spiral a galaxies set of with galaxies long with X-ray awould large exposures apparent constitute diameters, natural targets for a search for the 3.5 keV line from the DM consistent with all observations, andin can models explain of discrepancies darkhave that further cannot matter elucidated be directly the accounted decaying phenomenology for or of this annihilating scenario. into photons. Inpossible this — paper provided we the magnetictional field estimates. in the It galactic also73 centre requires cluster is the sample at ‘average’ of the ALP-to-photon highest] [1 generates conversion end to a probability of be highly for observa- distinctive slightly the morphology, smallerpc in than of which assumed the the in galactic signal [10].in plane. is [4,5] In highly This and this suppressed morphology masking case, within can the the 20 be scenario region easily close tested to by re-analysing the the galactic data plane. used θ JCAP04(2015)013 [ks] XMM t XMM n [ks] CXO t CXO – 22 – n Continued on next page i θ Table 3. NGC4698NGC4945NGC5005 SabNGC5170 SBc 73.4NGC5253 SABbNGC5506 Sc 90. 77. 1NGC5746 SBm 3NGC5775 Sa 1 85.3 90. SABb 30.4 SBc 3 249.9 90. 1 90. 5. 2 83.2 1 2 2 194. 33.4 1 1 49.7 37.3 10.2 1 88.4 1 59. 13.6 8 8 47. 31.9 1 371. 298. 47.2 NGC4039NGC4224NGC4244 SBmNGC4258 Sa 71.2NGC4388 ScNGC4395 SABb 7 75.8NGC4490 Sb 68.3 65.4 1NGC4565 Sm 425.2 4NGC4569 SBcd 1 90.NGC4631 Sb 90. 79. 10 2.NGC4666 SABa 2 46. 49.8 SBcd 4 70.8 3 90. SABc 273. 90. 2 48.2 1 2 69.6 8 2 79.3 98.9 1 1 41.4 3 39.7 103.9 158.3 62.8 4 5 60. 5. 1 92.1 1 154.9 115.8 1 1 66. 14.9 54.8 58.2 NGC2992NGC3034NGC3079 SaNGC3221 ScdNGC3396 SBcd 90. 76.9NGC3623 Sc 90.NGC3627 SBm 23 1NGC3628 SABa 65.7 1 90.NGC3877 SABb 90. 812.5 50.2NGC3972 Sb 1 67.5 1 26.9NGC4013 Sc 1 12 2 SABb 79.3 10 19.6 Sb 19.8 81.5 83.2 2 1.8 2 427.5 52. 502.7 1 5 1 90. 1 69.7 60.5 2 10.1 1 121.6 2 47.3 40.7 2 36.2 2 85.1 1 11.2 75.3 3 36.8 14.4 102. NGC0253NGC0520NGC0625 SABcNGC0660 Sa 90.NGC0891 SBmNGC0931 Sa 6 75.7 90.NGC1808 Sb 1NGC2683 Sbc 78.7 1 159.8NGC2798 Sa 90. 81.3 4NGC2799 Sb 50. 8NGC2841 SBa 61.1 3 83.9 1NGC2903 SBm 82.8 58.2 83.4 1 Sb 306.8 1 1 90. 174. 1 SABb 1 5. 2 67.1 65.2 43.4 1 13.1 26.6 2 1.8 1 2 5.2 2 34.1 2 5.2 151.6 94.8 30.4 1 1 100. 83.2 1 1 1 34.2 17.6 17.6 96.3 41.9 GalaxyIC2574IC2810 Type NGC0224 SABm SBab Sb 83. 75.2 1 72.2 1 105 11.4 939.9 15. 1 43 1 24.6 977.1 48.9 JCAP04(2015)013 [ks] XMM t XMM n [ks] CXO t CXO – 23 – n Continued on next page i θ Table 3. NGC3621NGC3683NGC3718 SBcdNGC4088 SBc 67.5NGC4178 Sa 68.8NGC4216 1 SABcNGC4217 Scd 71.2 66.5 3NGC4236 SABb 23.4 1 1 Sb 90. 90. 139. SBd 1 1 20.1 81. 5.4 90. 1 40. 1 5.3 73.7 11.2 NGC0988NGC1589NGC1741 ScNGC2552 SabNGC2748 Sm 68.7 80.3NGC2770 SABmNGC2783B Sbc 1 70.7 68. 1NGC3190 SABc Sb 1 1 68.1NGC3198 82.3 5.3 NGC3287 Sa 10.2 1 1 90.NGC3556 Sc 36. 8. SBd 87.8 1 SBc 30. 18.1 77.8 75.3 1 67.5 1 18.2 1 1 20.1 62.4 19.1 60.1 UGC12915ESO069-006 SBcESO137-001 SBbESO244-030 SBc 73.4 76.4ESO293-034 SABb 66.2ESO415-029 1 SBc 68.6 1ESO430-020 Sbc 1 1 74.6ESO432-006 SABc 40.IC0564 14.7 77.3 Sbc 70.3 1 141.9 NGC0024 10.1 3 1NGC0055 78.8 1 Scd Sc 10. 1 SBm 79.6 10.1 77.2 17.9 70.1 90. 16.3 1 1 1 15.2 43.8 9.7 NGC7090NGC7212NGC7331 ScNGC7582 SbNGC7590 Sbc 90.NGC7771 SBab 76.4PGC014370 Sbc 70. 68.2 2 1PGC037477 Sa Sc 69.4 2 1PGC044990 Sb 57.4PGC046710 Sc 66.7 20.2 1 78.8PGC093080 SBb 19.6 30.1 76.8 1PGC1110773 Sc 2 3 83.8 Sab 81.2 1 30.1 4 3 3 1 17.2 1 70.6 71.8 8.1 77.4 100.7 2 14.2 1 8 15.1 130. 30.8 1 7.2 1 5 50.5 233. 50. 1 32.1 2 54.2 331. 1 1 29. 136.8 43.1 13.1 GalaxyNGC5793NGC5907 Type NGC6118 Sb SABc Sc 90. 78. 2 2 68.7 1 30.1 40.8 8.1 6 1 1 155.1 25.8 26.5 JCAP04(2015)013 [ks] XMM t XMM n [ks] CXO t CXO – 24 – n Continued on next page i θ Table 3. ESO209-012ESO365-001 SaESO365-016 ScESO471-006 SBab 90.ESO491-021 SBm 66.4 90.IC1504 SBab 90.IC1537 79.IC1959 Sb Sc SBm 80.8 65.7 90. 1 1 1 1 20.4 1 26.3 14.9 19.9 20.3 1 1 1 18.6 33.6 14. PGC2793298 SaUGC01934UGC02238 SbcUGC02626 90. SmUGC03326 Sa 90.UGC03995 1 Sc 68.9ESO121-006 1 SbcESO140-043 Sc 90. 1 91. ESO154-023 SBb 90. 66.4 1ESO195-005 SBm 9. 90. 15.1 72.8ESO208-034 1 Sa 1 90. SBab 25.5 75.4 80.1 90. 11. 2 1 1 2 49.4 35 15. 18.7 581.3 29.2 NGC7591NGC7673NGC7753 SBbcPGC001221 Sc 66.9PGC019078 SABb SBcPGC027508 1 82.1 E? 68.2PGC038430 73.3 SBab 1PGC046114 1 Sd 1 73. 90. 5. PGC046133 SbcPGC086247 12.2 Sbc 59.4 75.8 1 2PGC100170 82.8 Sbc 30. 1 80.5 SBbc 1 14.8 48.9 90. 71.1 1 15. 1 1 15. 15. 16.3 25.6 NGC4527NGC4772NGC4848 SABbNGC4939 Sa 81.2NGC5394 Sc 1NGC5395 Sbc 67.3NGC5674 SBb 73.9 70.1 1NGC6027C SABb 5. 70.8NGC6503 SABc 1 66.1 SBc 1NGC6872 80.2 1 5.2 1NGC6925 Sc 86.8 29. 1NGC7541 SBb 15. 16.1 1 Sbc 16.1 73.5 72.5 SBc 5.1 84.1 2 2 70. 74.8 1 1 15.4 76.3 10. 39.5 GalaxyNGC4355NGC4419 Type NGC4438 SABa Sa 68. Sa 2 84.5 73.2 2 26.7 1 6. 25.4 JCAP04(2015)013 [ks] XMM t XMM n [ks] CXO t CXO – 25 – n Continued on next page i θ Table 3. NGC5073NGC5356NGC5899 SBcNGC6045 SABbNGC6323 Sc 90. 90.NGC6810 SBcNGC6814 Sab 68.9 85.3NGC6926 Sab 68.3 SABb Sc 90. 85.6 78.1 1 2 2 3 53.6 38.7 2 29.6 2 1 75.2 25.7 1 36.1 48.7 11.8 NGC4235NGC4302NGC4319 SaNGC4330 ScNGC4437 SBab 90.NGC4536 Sc 72.5 90.NGC4605 ScNGC4634 SABb 78.8NGC4686 SBc 73. 90.NGC4700 SBcNGC4845 Sa 70. 80.5 SBc Sab 82.7 90. 1 7 90. 2 1 13.1 246.4 100.8 1 1 31.4 1 3 34.2 114.3 2 1 135.9 8. 2 32.6 87.3 29.7 NGC3044NGC3227NGC3281 SBcNGC3735 SABaNGC3746 Sab 90. 68.3NGC3753 Sc 71.7NGC3786 SabNGC3788 Sab 83.5 66.6NGC3976 SABaNGC4157 SABa 90. 65.2NGC4173 SABb 86.1 SABb 81.6 SBcd 90. 4 2 90. 1 162.6 38. 2 2 23.7 1 2 21.9 1 61. 1 29.5 61. 1 29.5 1 14.4 62.7 12.9 NGC0092NGC0192NGC0675 SaNGC0716 SBaNGC0784 Sa 69.9 76.2NGC1134 SaNGC1311 SBd 73.9NGC1320 Sb 76.2 90.NGC1511 SBmNGC1512 Sa 77.2 90.NGC2369 SabNGC2613 Sa 80.5 73.7 Sa 1 Sb 68.3 1 90. 1 90. 48. 1 48.9 1 39.9 1 1 25.6 18. 1 1 24.8 14.8 1 17.1 44.9 2 2 71.6 47.5 75.2 GalaxyIC4518AIC4518B Type IC5052 Sc Sc 73.3 SBcd 90. 90. 2 2 1 37.1 37.1 19.5 JCAP04(2015)013 ] keV 5 . 3 [ks] ]. arXiv:1408.3531 (2014) 251301 ]. ]. 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