arXiv:1512.01239v2 [astro-ph.HE] 9 Mar 2016

n n htno akmte atcewt aso rud7 around of mass a with about particle of matter lifetime inc a dark decay and a keV radiative of two-body photon a one with ing associated be might line 6Ags 2018 August 16 MNRAS oasye l 2009 al. et Boyarsky 2014 Profumo & Jeltema nteXrydt rmidvda n tce observations brevity) stacked for and ( 3.57 line” individual galaxies – keV from of 3.50 3.5 data clusters between “the energy X-ray of an as the with indicated in line (hereafter a keV of detection The INTRODUCTION 1 e n nteMlyWy hspsiiiywsiiilydisc initially was possibility This of Way. clusters Milky by in the both in a line and keV XVIII) ies 3.5 (K the ions to counterpart Potassium plausible He-like from lines de-excitation † ⋆ photospheric by than out magnitude pointed of recently order as mor abundances, one to solar abunda about up K by by coronal larger Additionally, lines magnitude. are de-excitation of XVIII order one K than the of brightness the ( ( center tic eprtr oesbae oad ihtmeaue.Tel The in temperatures. demonstrated high as towards biased on models and abundances, temperature solar K photospheric on relied that dance liigtemsignnbroi atri h nvre(s the in of matter that non-baryonic beyond missing goes the motivation plaining whose candidates matter model neutrino dark sterile in counterpart theoretical natural el Jeltema Line Tesla keV 3.5 the for Confidence Origin 99% Decay the Matter at Dark out a rule Level of Observations XMM Deep 1 c oasye l 2014 al. et Boyarsky eateto hsc n at rzIsiuefrParticle for Institute Cruz Santa and Physics of Department [email protected] [email protected] 00TeAuthors The 0000 uble al. et Bulbul etm Profumo & Jeltema 000 etm rfm 2015 Profumo & Jeltema 0–0 00)Pern 6Ags 08Cmie sn MNRA using Compiled 2018 August 16 Preprint (0000) 000–000 , ( 2014 etm Profumo & Jeltema o review). a for , 1 ae netmtso h eurdKabun- K required the of estimates on based ) sehowever (see ) ⋆ ( a rgee iepeditrs:the interest: widespread triggered has ) Profumo Stefano and 2015 uble l 2014 al. et Bulbul 6 − one u al nta atomic that on early out pointed ) 8 × 10 lsisrmna ie;teadto fa complet which of are addition background, range the particle lines; energy the instrumental this w plus modeling in line law data No power The Draco. unfolded detectors. galaxy PN spheroidal the or dwarf the of observations e words: Key an galaxies d of a C.L.. clusters out 99% of rules observations than in flux found line line the keV on 3.5 limit upper corresponding The fit. esace o nXryln teege rud35kVi dee in keV 3.5 around energies at line X-ray an for searched We ABSTRACT csooy)dr matter dark (cosmology:) n,tnaiey rmM31 from tentatively, and, ) 27 ( etm rfm 2015 Profumo & Jeltema 2014 e.Sc atcehsa has particle a Such sec. ,atfiilysuppress artificially ), hlise al. et Phillips ,fo h Galac- the from ), -as aais -as aais lses -as ISM X-rays: clusters; galaxies: X-rays: galaxies; X-rays: ,acasof class a s, hsc nvriyo aiona at rz A904 USA 95064, CA Cruz, Santa California, of University Physics ( 1 ee.g. ee 2015 galax- multi- arded † atter, nces lud- ea re ex- K ). e ; inlsrnt clsnntiilywt h nertdd integrated the with non-trivially scales strength signal in reported Perseus in line keV 3.5 the of phology l keV 3.5 the for culprit the plausible. as quite XVIII present K at for appears case the result, a As ( 2015 fro originates line keV 3.5 the high- a of that that indicates is processes pro possibility exchange density ditional charge matter of dark study Galactic recent cored A for dark even a excluding origin and decay lines, m emission the elemental with bright of correlation ogy notable and a galaxies finding of center, cluster Galactic Perseus the the from emission hypothe keV decay 3.5 the matter dark the compat with the Finally, morphology questioning line and the K, of to ity ascribed keV be 3.5 naturally the that could confirming clusters, X-ray-bright from data ( ( aeslu osadnurlhdoe)t h rudsae( state ground the to hydrogen) neutral and ions sulfur bare a r tl optbewt o-tnadoii o h 3 the for origin non-standard magne in ( a conversion particle with axion-like Notably, compatible line. keV still are far t line. failed keV also 3.5 and a XVIII, for K evidence fain e.g. any too from be line would detectable a emission produce thermal the where systems groups, line. the for origin decay matter dark result a null constrained a reporting galaxies, spheroidal dwarf of tions a rgnfrte35kVln a loemerged. also has line keV 3.5 the for origin cay akmte ( matter dark 2015 2014 al. et Cicoli 2015 2014 diinlcrusata vdneaantadr atrd matter dark a against evidence circumstantial Additional ti motn oakoldeta ulrslsotie so obtained results null that acknowledge to important is It ). ;ohrpsiiiisicue o xml,ieatcexc inelastic example, for include, possibilities other ); galaxy and galaxies of observations stacked analyzed ) observa- XMM archival stacked, in line the for searched ) n alo tal. et Carlson ∼ V rniin ppltdb hretase between transfer charge by (populated transitions XVI S 3 ikenr&Wie 2014 Weiner & Finkbeiner . 5 e iefauegvsn mrvmn othe to improvement no gives feature line keV ; lae ta.2015 al. et Alvarez ( 2015 tde ndti h opooyof morphology the detail in studied ) nteGlci etra greater at Center Galactic the in d ra tal. et Urban r atrdcyoii o the for origin decay matter ark p, oiae tteeenergies, these at dominates sfudi ihrteMOS the either in found as l ossetwt single, a with consistent ely ∼ ol erdc h mor- the reproduce could ) 1 .I l uhisacs the instances, such all In ). . 6 scXMM-Newton Msec ie identification; line: ; ( 2015 L S A tde Suzaku studied ) T ayhve al. et Malyshev E nesne al. et Anderson tl l v3.0 file style X alo tal. et Carlson hthighly that r matter ark ue al. et Gu i fields tic set a m orphol- matter signal find o ad- n from files. ibil- ited to t sis. ine e- .5 2 T. Jeltema and S. Profumo

0.3 0.08 −1 −1 keV keV

−1 0.06 −1 0.2

0.04

0.1 0.02 normalized counts s normalized counts s

−1 0 −1 0 0.01

2×10 keV −3 keV −1 −1 5×10−3

0 0 −5×10−3 −2×10−3 −0.01 normalized counts s normalized counts s 3 3.5 4 4.5 3 3.5 4 4.5 Energy (keV) Energy (keV)

Figure 1. Left: Combined MOS spectrum and residuals in the 2.5-5.0 keV energy range fit to an unfolded, single power law. For visual effect here the spectrum has been binned by a factor of five. Right: Combined PN spectrum and residuals (with a similar factor of five binning) in the 2.5-5.0 keV energy range fit to an unfolded single power law plus an instrumental line due to Ti Kα emission at 4.51 keV. A weaker Ti Kβ line can be seen at 4.93 keV but has no effect on the 3.5 keV line constraints. mass along the line of sight, or it depends sensitively on astrophys- using standard procedures and utilizing the XMM SAS1 and ESAS ical conditions such as the magnetic field strength. (Snowden et al. 2008; Kuntz & Snowden 2008) software packages. Lovell et al. (2015) used N-body simulations from the Aquar- Starting from the Observation Data Files, the raw EPIC data was ius project (Springel et al. 2008) to estimate the flux ratio for a pipeline-processed with the emchain and epchain tasks. Flare standard decay process across different targets, includ- filtering was carried out with the ESAS tasks mos-filter and ing for the Draco (dSph) and the Galactic pn-filter; these time periods of increased particle background center (GC). This ratio has a certain statistical distribution, which due to soft protons can lead to background levels elevated by two depends on the choice of the placement of the observer. The central orders of magnitude and are thus removed from the data. Unfortu- finding of that study is that a 1.3 Ms long XMM-Newton observa- nately, in the case of Draco particle background flaring was signif- tion of the Draco dSph would enable the discovery or exclusion at icant in many of the observations. For the two MOS detectors, two the 3σ level of a dark matter decay interpretation of the 3.5 keV observations (ObsID 0603190401 and 0770190601) were almost signal. entirely contaminated by flaring, and we removed these from our Here, we utilize recent, deep archival XMM-Newton observa- final data set; the other observations had reduced usable exposure tions of the Draco dSph to test a dark matter decay origin for the times. The net exposure time after filtering was a little over one 3.5 keV line. We find no evidence of a line in either the MOS or Msec for each MOS detector with a total time for both detectors PN data, and we are able to rule out a dark matter decay origin at of 2.1 Msec. The PN detector is typically more effected by particle greater than the 99% confidence level. flaring than the MOS detectors, and we found that only 20 of 31 The remainder of this manuscript has the following structure: observations had flares satisfactorily removed by pn-filter; for we describe the XMM observations and data reduction in the fol- these observations the net usable exposure time for PN was 0.58 lowing section 2; we then describe our flux calculation and compare Msec. with the flux limits from the XMM MOS and PN data in section 3, Point sources were detected and removed separately from each and we present our conclusions in the final section 4. observation using the ESAS task cheese; point source detection was run on broad-band images (0.4-7.2 keV) with a flux limit of − − − 10 14 erg cm 2 s 1 and a minimum separation of 10 arcsec. Low exposure regions are likewise masked by cheese. Spectra were extracted from the full field-of-view from each detector in each 2 XMM DATA ANALYSIS flare-filtered observation; however, for the MOS1 detector CCDs 3 and 6 were excluded due to micrometeroid damage. Spectra and Draco was observed by XMM-Newton in 31 separate observations, 5 in 2009 (PI Dhuga) and 26 in 2015 (PI Boyarsky), with individ- ual exposure times ranging from 17 to 87 ksec and a total time in all observations of 1.66 Msec. We reprocessed all 31 observations 1 http://xmm.esac.esa.int/sas/

MNRAS 000, 000–000 (0000) Deep XMM Observations of Draco rule out a dark matter decay origin for the 3.5 keV line 3

-6 -6 2.5×10 3.5×10 Lovell+ Lovell+ Wolf+ -6 Wolf+ Geringer-Smith+ 3.0×10 Geringer-Smith+ -6 Bulbul+ PN Bulbul+ MOS 2.0×10 ] Boyarsky+ M31 ] -1 -1 × -6 s Boyarsky+ Perseus s 2.5 10 -2 -2 -6 1.5×10 -6 Bulbul+, PN Bulbul+, MOS 2.0×10 Boyarsky+, M31 68% C.L. Boyarsky+, Perseus -6 -6 1.5×10 1.0×10

-6 1.0×10 Line Flux [cts cm Line Flux [cts cm -7 99% C.L. 5.0×10 -7 5.0×10 90% C.L. 0.0 0.0 3.3 3.4 3.5 3.6 3.7 3.3 3.4 3.5 3.6 3.7 Line Energy [keV] Line Energy [keV]

Figure 2. Left: Limits on the flux of a line in the energy range between 3.3 and 3.7 keV from MOS observations of the Draco dSph, at the 68%, 90% and 99% C.L. (green, red and black lines, respectively) and predictions for the flux of a 3.5 keV line assuming a dark matter decay origin for the line detected at that energy from stacked clusters of galaxies and from the center (see text for details). The horizontal black lines indicate the 1σ energy range for the line position as inferred by Boyarsky et al. 2014 for Perseus (3.50 ± 0.04 keV) and for M31 (3.53 ± 0.03 keV) and by Bulbul et al. 2014 from cluster observations (3.57 ± 0.02 and 3.51 ± 0.03 keV for their “full sample” MOS and PN results, resepctively); Right: same, for PN observations (note the difference in vertical scale). corresponding redistribution matrix files (RMF) and ancillary re- 3 FLUX LIMITS AND CONSTRAINTS ON DARK sponse files (ARF) for the 0.4-7.2 keV range were created using MATTER DECAY mos-spectra and pn-spectra in the ESAS package. The in- We utilize three distinct predictions for the 3.5 keV line flux that dividual spectra and response files were co-added using the rou- should have been observed with the XMM observations described tines mathpha, addrmf, and addarf in the FTOOLS package above for a dark matter decay origin . The first one makes use of the (Blackburn 1995). Combined RMF and ARF files were weighed by results of Lovell et al. (2015), which calculated the flux expected the relative contribution of each observation to the total exposure from a 14 arcmin angular region around Draco given the brightness time. The spectra and responses for the MOS1 and MOS2 cam- of the 3.5 keV line observed from the and the ratio eras were combined in to a single summed MOS spectrum, while of the flux from Draco-like halos and from the Galactic center as the spectra and responses for the PN detector were combined sepa- extrapolated from the Aquarius simulation. The resulting distribu- rately. tion in predictions is bracketed by the range Spectral modeling employed the energy range between 2.5 − × −6 −2 −1 keV and 5 keV. This energy range was chosen to exclude strong F = (1.0 5.2) 10 cts cm s , instrumental emission lines while being much, much broader than where the lower and upper values bracket 95% of the predic- the energy resolution of the detectors (∼ 100 eV). At these en- tions, and with the most-probable value being F = 2.3 × ergies, the X-ray background is dominated by the quiescent parti- 10−6 cts cm−2 s−1 (see especially their Appendix C3 for addi- cle background (Kuntz & Snowden 2008) which we model with an tional details on assumptions and method). We calculated that the unfolded, power law (no vignetting) in XSPEC (version 12.8.1p, point source masking we adopt and the non-uniform coverage (e.g. Arnaud 1996). As shown in Fig. 1, the combined MOS spectrum from the lost MOS CCDs and chip gaps) described in the previous in the 2.5-5 keV range is well fit by an unfolded, single power section suppress the predicted flux to 77% of its un-masked value law alone with reduced χ2 = 0.96 (χ2 = 475/497 degrees of (we neglect the additional signal from the annulus between 14 and freedom). Adding a Gaussian line between 3.4 and 3.6 keV gives 15 arcmin). We calculated the fraction of masked signal employ- no improvement to the fit, and a line at these energies with a flux ing the dark matter density profile and distance to Draco quoted − − − greater than ∼ 10 6 photons cm 2 s 1 is excluded, as shown in in Abdo et al. (2010). We verified that the impact on the masking Fig. 2. The confidence contours in Fig. 2 are determined based on fraction of varying the parameters in the dark matter density profile the change in the fit statistic when stepping over the relevant pa- and the distance within their 2-σ range is in all cases smaller than rameters using the steppar command in XSPEC. The combined 0.1%. We show the resulting range of expected fluxes in Fig. 2 with PN spectrum is well fit by an unfolded power law plus an instru- the vertical blue bar, and indicate the central value with a full blue mental line due to Ti Kα emission (4.51 keV), which we model as square. a narrow Gaussian (Fig. 1, right). The reduced χ2 for this fit is 0.99 We additionally considered two alternate predictions for the (χ2 = 490/495 degrees of freedom). Again, adding a Gaussian flux expected in the data we analyze for the decaying dark mat- line between 3.4 and 3.6 keV gives no significant improvement to ter scenario. We followed the procedure outlined in Malyshev et al. the fit. The fit is somewhat improved by adding a second instru- (2014). There, two alternate determinations of the mass within half- mental line, Ti Kβ, at 4.93 keV, but this feature has no effect on the light radius were adopted to estimate the integrated line of sight 3.5 keV line constraints. As can be seen from Fig. 2, right the upper dark matter column density for Draco, based on the results of the limit on the flux of a line near 3.5 keV from the PN data is weaker analyses of Wolf et al. (2010) and Geringer-Sameth et al. (2015). than from the MOS data given the shorter usable exposure time but Malyshev et al. (2014) then proceeded to add, for the direction of does serve as additional confirmation of the lack of a 3.5 keV line Draco, the flux from dark matter within the Milky Way, and added from Draco. to it the prediction for the component from the Draco dSph itself.

MNRAS 000, 000–000 (0000) 4 T. Jeltema and S. Profumo

For the former, Malyshev et al. (2014) presents a “mean” flux based essentially the same data set as this work. They come to a similar on the “favored NFW” Milky Way dark matter halo of Klypin et al. conclusion that no 3.5 keV line is detected in Draco, though their (2002), as well as a very conservative “minimal” model based on limit on the flux of the line is less stringent than ours. The main a “maximal disk” halo structure. We choose to show our predic- difference appears to stem from the fact that they find a mild ex- tions for the flux in Fig. 2 for the mean flux from the Milky Way, cess in the PN data which we do not see. Here we comment briefly but it is a straightforward exercise (and one that does not impact on some of the differences in the two analyses. Ruchayskiy et al. our results or conclusions qualitatively) to rescale them for the (2015) make three comments on our analysis. 1) We do not include minimal Milky Way model. The predicted flux was normalized, an extragalactic background power law in addition to the particle as in Malyshev et al. (2014) and in Lovell et al. (2015), to the pa- background; 2) the ∼ 1σ excesses in the MOS spectrum near 3.35 rameters corresponding to the best-fit point of the cluster observa- keV and 3.7 keV might be due to un-modeled weak instrumental tions of Bulbul et al. (2014). We show the predictions for the Draco lines (from K Kα and Ca Kα at 3.31 and 3.69 keV); 3) we do not halo determination in Wolf et al. (2010) with brown diamonds and jointly fit the MOS and PN data. We have now tried all three of Geringer-Sameth et al. (2015) with purple triangles. The uncertain- these variations and find that they all have a negligible effect on ties we show in the figure reflect the uncertainties from the determi- our results. Adding additional lines or background components as nation of the halo parameters as in Malyshev et al. (2014). As we in points 1) and 2) is not warranted by the data nor does it signifi- did for the predictions from Lovell et al. (2015), we corrected the cantly improve our fits when done. In fact, we find that when we do predicted flux quoted in Malyshev et al. (2014) for masking in our add these components our flux limit on a line near 3.5 keV in the observations, and for the larger, in this case, angular region we uti- MOS data is actually strengthened, albeit slightly, lowering the flux lize compared to the flux predictions in Malyshev et al. (2014). We limit by 10%. We note that when adding an additional power law illustrate our results in Fig. 2. We indicate with green, red and black for the extragalactic background in addition to the unfolded power lines the 68%, 90% and 99% Confidence Level (C.L.) limits on the law for the particle background, we expanded the energy range to maximal allowed flux associated with a line at the energy indicated 2.5-7 keV and added lines for the strong Cr, Mn, and Fe instrumen- by the x-axis. We also show the predictions for the line flux de- tal lines in this range, but again we find no excess near 3.5 keV. scribed above as well as the range of energies for the line reported Here the power law components are free to vary; the best fit pho- from cluster observations as described in Bulbul et al. (2014) and ton indices are 1.5 for the extragalactic power law and 0.33 for the the range obtained by Boyarsky et al. (2014) from observations of unfolded power law with a reduced χ2 of 0.99 (χ2 = 876/885 the Perseus cluster and of M31. degrees of freedom). As can be seen in Fig. 2, the lack of a detected line in the Results from combined fits to the MOS and PN data must MOS data rule out at higher than 99% confidence level a line be interpreted with care as there are known offsets in the relative with even the most conservative predicted fluxes based on a con- calibration of the two camera types. In particular, fits to a stack servative range of possible density profiles for the Draco dwarf. of bright sources show an offset of 5-8% between MOS and PN Specifically, the lower limit on the predicted Draco line flux of (Read et al. 2014) above 3 keV, which is similar to or larger than Lovell et al. (2015) based on the brightness of the line observed the ratio of the predicted 3.5 keV line flux to the neighboring con- in the Galactic Center is excluded at 99.1%; the lower limit on the tinuum. In performing a joint fit to the MOS and PN spectra, we predicted flux given the observed stacked cluster line flux are ex- separately fit the continuum models for the two instruments, but cluded at better than 99.999% for either the Wolf et al. (2010) or the jointly fit the 3.5 keV line energy and flux. We again find no excess Geringer-Sameth et al. (2015) profiles. Therefore, a generic dark near 3.5 keV. Our limit on the flux of a line near 3.5 keV is weak- matter decay origin of the 3.5 keV line feature is highly unlikely. ened only slightly (by 25-30%) from the MOS-only limit shown in In Fig. 3, we show constraints on the sterile neutrino param- the left panel of Fig. 2, and we still exclude the most conservative eter space in terms of the particle’s mass ms and mixing angle predictions from Lovell et al. (2015) at the 99% confidence level. with active neutrinos θ given the line flux limits from the MOS The primary reason that Ruchayskiy et al. (2015) quote a Draco observations, in the relevant mass range for a dark mat- weaker limit on the flux of a line from Draco appears to be due ter decay interpretation of the 3.5 keV line. The cyan shaded re- to the fact that they find a ∼ 2σ excess in the PN which is not gion is excluded at the 2σ level, and assumes the central value present in our analysis. It is unclear why they find an excess where for the Geringer-Sameth et al. (2015) dark matter halo parame- we do not, but we note that in their spectral fits they include data ters for Draco, and the most conservative Milky Way halo con- up to 10 keV where the effective area is both rapidly dropping and sidered in Malyshev et al. (2014) (corresponding to the “maximal a factor of ∼ 4 lower than at 3 keV for PN, and more than an order disk model” of Klypin et al. (2002)). The blue shaded region, in- of magnitude lower for MOS. In addition, their background model, stead, adopts the default “favored NFW” Milky Way dark matter given the large energy range, includes 13 line components and two halo density profile (Klypin et al. 2002). power laws compared to our single power law. Taking the most conservative possible assumptions both for the flux from Draco and from the Milky Way (corre- sponding to the predictions of Wolf et al. (2010) for the flux from Draco and the most conservative Milky Way halo of Klypin et al. 4 DISCUSSION AND CONCLUSIONS (2002)), we are able to set a lower limit on the lifetime of a 7 keV 28 sterile neutrino decaying into a 3.5 keV line of τ > 2.7 × 10 Using ∼ 1.6 Msec observations of the Draco dSph with XMM- 2 s (95% C.L.), corresponding to a mixing angle sin (2θ) < 1.6 × Newton we were able to obtain one of the most stringent constraints −11 10 (95% C.L.). Our most conservative limits are thus more than on a dark matter decay origin for the 3.5 keV line observed from a factor 4 below the favored mixing angle predicated by a dark clusters of galaxies and from the Milky Way center. Our results rule 2 matter decay interpretation of the 3.5 keV line signal (sin (2θ) ≈ out a dark matter decay interpretation with greater than 99% C.L., −11 7 × 10 , Bulbul et al. 2014). and, under very conservative assumptions on the relevant dark mat- After our paper appeared, Ruchayskiy et al. (2015) analyzed ter density profiles, imply a lower limit on the dark matter lifetime

MNRAS 000, 000–000 (0000) Deep XMM Observations of Draco rule out a dark matter decay origin for the 3.5 keV line 5

of the Pacific Conference Series Vol. 101, Astronomical Data Analysis Software and Systems V. p. 17 -10 Blackburn J. K., 1995, in Shaw R. A., Payne H. E., Hayes J. J. E., eds, 10 Astronomical Society of the Pacific Conference Series Vol. 77, Astro- nomical Data Analysis Software and Systems IV. p. 367 Boyarsky A., Ruchayskiy O., Shaposhnikov M., 2009, Ann.Rev.Nucl.Part.Sci., 59, 191 )

θ Boyarsky A., Ruchayskiy O., Iakubovskyi D., Franse J., 2014,

(2 Physical Review Letters, 113, 251301 2 Bulbul E., Markevitch M., Foster A., Smith R. K., Loewenstein M., Randall sin S. W., 2014, ApJ, 789, 13 Carlson E., Jeltema T., Profumo S., 2015, JCAP, 1502, 009 Cicoli M., Conlon J. P., Marsh M. C. D., Rummel M., 2014, Phys. Rev. D, -11 10 90, 023540 Finkbeiner D. P., Weiner N., 2014, preprint, (arXiv:1402.6671) MOS, full sample (Bulbul+) PN, full sample (Bulbul+) Geringer-Sameth A., Koushiappas S. M., Walker M., 2015, ApJ, 801, 74 Gu L., Kaastra J., Raassen A. J. J., Mullen P. D., Cumbee R. S., Lyons D., Stancil P. C., 2015, preprint, (arXiv:1511.06557) 6.6 6.8 7 7.2 7.4 m [keV] Jeltema T., Profumo S., 2014, preprint, (arXiv:1411.1759) s Jeltema T. E., Profumo S., 2015, Mon. Not. Roy. Astron. Soc., 450, 2143 Klypin A., Zhao H., Somerville R. S., 2002, Astrophys. J., 573, 597 Figure 3. Constraints on the parameter space of sterile neutrinos, defined by Kuntz K. D., Snowden S. L., 2008, Astronomy & Astrophysics, 478, 575 the particle’s mass ms and mixing angle with active neutrinos, θ. The cyan- Lovell M. R., Bertone G., Boyarsky A., Jenkins A., Ruchayskiy O., 2015, shaded region is excluded, at the 2σ level (∼95% C.L.), by Draco MOS MNRAS, 451, 1573 observations, using the most conservative Milky Way dark matter density Malyshev D., Neronov A., Eckert D., 2014, Phys. Rev., D90, 103506 profile considered in Malyshev et al. (2014), while the blue-shaded region Phillips K. J. H., Sylwester B., Sylwester J., 2015, Astrophys. J., 809, 50 employs the nominal “favored NFW” profile, which we also use for Fig. 2. Read A. M., Guainazzi M., Sembay S., 2014, A&A, 564, A75 Ruchayskiy O., et al., 2015, preprint, (arXiv:1512.07217) Snowden S. L., Mushotzky R. F., Kuntz K. D., Davis D. S., 2008, × 28 of τ > 2.7 10 s at 95% C.L. for a dark matter mass of 7 keV Astronomy & Astrophysics, 478, 615 radiatively decaying to a two-body final state with one photon. Springel V., et al., 2008, Mon. Not. Roy. Astron. Soc., 391, 1685 In view of the results presented here, and in view of the recent Urban O., Werner N., Allen S. W., Simionescu A., Kaastra J. S., Strigari re-assessment of the potassium abundance (Phillips et al. 2015), L. E., 2015, MNRAS, 451, 2447 we conclude that the most probable counterpart to the 3.5 keV Wolf J., Martinez G. D., Bullock J. S., Kaplinghat M., Geha M., Mu˜noz line observed towards the Milky Way center and from individual R. R., Simon J. D., Avedo F. F., 2010, Mon. Not. Roy. Astron. Soc., and stacked observations of clusters of galaxies are atomic de- 406, 1220 excitation lines of the K XVIII ion. Charge-exchange processes might also provide an alternate astrophysical explanation (Gu et al. 2015). Scenarios advocating new physics where a 3.5 keV signal is suppressed in dwarf galaxies, such as an axion-like particle conver- sion to 3.5 keV photons in the presence of a magnetic field, are not ruled out unless Occam’s razor is advocated. Future observations of clusters and of the Galactic center with Astro-H remain a priority to pinpoint the physical origin and the nature of the 3.5 keV line, while, in view of our results, additional deep observations of local dwarf galaxies with current or future telescopes are unlikely to advance our understanding of this partic- ular feature.

ACKNOWLEDGMENTS We would like to thank the referee for their valuable comments on our paper. TJ is partly supported by NSF AST 1517545. SP is partly supported by the US Department of Energy, Contract DE- SC0010107-001.

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