Searching for the 3.5 keV Line in the Deep Fields with Chandra: the 10 Ms observations

TL;DR

This study searches for a 3.5 keV emission line in deep Chandra X-ray observations, finding marginal evidence that could suggest sterile neutrino decay, but remains inconclusive due to statistical limitations.

Contribution

First systematic search for the 3.5 keV line in deep Chandra data, providing constraints on sterile neutrino dark matter and discussing potential astrophysical origins.

Findings

Marginal 3.5 keV line detection at 2.5-3 sigma significance.

Line flux consistent with previous detections in Galactic center.

Results support sterile neutrino decay as a possible origin.

Abstract

In this paper we report a systematic search for an emission line around 3.5 keV in the spectrum of the Cosmic X-ray Background using a total of $\sim$10 Ms Chandra observations towards the COSMOS Legacy and CDFS survey fields. We find a marginal evidence of a feature at an energy of $\sim$3.51 keV with a significance of 2.5-3 $\sigma$, depending on the choice of the statistical treatment. The line intensity is best fit at $8.8\ \pm\ {2.9}\times10^{-7}$ ph cm$^{-2}$s$^{-1}$ when using a simple $\Delta\chi^2$ or $10.2\ ^{+0.2}_{-0.4} \times10^{-7}$ ph cm$^{-2}$s$^{-1}$ when MCMC is used. Based on our knowledge of $Chandra$, and the reported detection of the line by other instruments, an instrumental origin for the line remains unlikely. We cannot though rule out a statistical fluctuation and in that case our results provide a 3$\sigma$ upper limit at 1.85$\times$10$^{-6}$ ph cm$^{-2}$s$^{-1}$. We discuss the interpretation of this observed line in terms of the iron line background; S {\sc XVI} charge exchange as well as potentially from sterile neutrino decay. We note that our detection is consistent with previous measurements of this line toward the Galactic center, and can be modeled as the result of sterile neutrino decay from the Milky Way for the dark matter distribution modeled as an NFW profile. For this case, we estimate a mass m$_{\nu}\sim$7.01 keV and a mixing angle sin$^2$(2$\theta$)= 0.83--2.75 $\times 10^{-10}$. These derived values are in agreement with independent estimates from galaxy clusters; the Galactic center and M31.

Tables

Table 1. Table 1 [2.4-7] keV net counts and exposures

	SIGNAL	BACKGROUND	EXPOSURE
	(counts)	(counts)	Ms
CDFS	115373	1989189	5.57
CCLS	131826	1220611	3.59
Total	247199	3209800	9.16

Table 2. Table 2 Best-fit emission line parameters from the Joint Fits of Deep Field CXB Spectra obtained withm the MCMC method.

Energy	Flux
keV	10-6 ph cm-2 s-1
2.51 $\pm$ 0.01	52.80 $\pm$ 19.64
3.51 $\pm$ 0.02	1.02 $\pm$ 0.41
4.37 $\pm$ 0.03	1.12 $\pm$ 0.29
6.38 $\pm$ 0.04	1.98 $\pm$ 0.55
${\chi }^2$ (dof)

Table 3. Table 4 Predicted S XVI Charge exchange transitions lines.

Transition	Energy	IE/I2.62	I(E)
	keV	10-6 ph/cm2.
2$\to$1	2.621	1.0	2.98
3$\to$1	3.106	0.142	1.45
4$\to$1	3.276	0.050	0.64
5$\to$1	3.354	0.025	0.51
6$\to$1	3.397	0.016	0.64
7$\to$1	3.423	0.011	1.02a
8$\to$1	3.434	0.120	1.02a
9$\to$1	3.451	0.074	1.02a

Equations

$$S_{3.5,Nu}=F_{3.5,Nu}/(\kappa (E)\ast 1.43\times 10^{-5}),$$

$$I_{DM}(\theta )=I_{DM,GC}$$

$$r(l,\theta )=\sqrt{l^2+d^2-2ldcos(\theta )}$$

$${\rho }_{DM}=\frac{{\rho }^{\ast }}{x(1+x{)}^2}$$

$$\begin{array}{r}{\Sigma }_{\mathrm{DM},\mathrm{High}}=0.0362\mathrm{gm}\mathrm{c}{\mathrm{m}}^{-2};\\ {\Sigma }_{\mathrm{DM},\mathrm{Low}}=0.0109\mathrm{gm}\mathrm{c}{\mathrm{m}}^{-2}.\\ \end{array}$$

$$\begin{array}{r}{\sin }^{2}2\theta \times (\frac{m_{\nu }}{11\mathrm{keV}}{)}^4\times \frac{{\Sigma }_{\mathrm{DM}}}{\mathrm{gm}\mathrm{c}{\mathrm{m}}^{-2}}=\\ (\frac{I_{\nu }}{1.45\times 10^{-4}})\mathrm{photons}\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}\mathrm{arcse}{\mathrm{c}}^{-2},\\ \end{array}$$

$${\tau }_{\mathrm{DM}}=7.2\times 10^{29}\sec (\frac{10^{-8}}{{\sin }^{2}2\theta })(\frac{1\mathrm{keV}}{m_{\nu }}{)}^5$$

Full text

1. Introduction

Astrophysical and cosmological observations of gravitational interactions of visible baryonic matter provide overwhelming evidence for the existence of an additional dominant, component of non-luminous matter, referred to as dark matter (see e.g. Rubin & Ford, 1970). Extensive direct and indirect searches for this ubiquitous matter have so far failed to detect it, and, its nature remains unknown. The majority of this unseen component is inferred to be cold and collisionless, however, a warmer component can also be accommodated to account at least partially to the overall mass budget of dark matter. X-ray observations of dark matter-dominated objects, such as galaxies and clusters of galaxies, provide a unique laboratory for searching for the decay or annihilation of a viable warm dark matter candidate, namely sterile neutrinos (Dodelson & Widrow, 1994; Dolgov & Hansen, 2002; Abazajian et al., 2001; Boyarsky et al., 2006).

An unidentified emission line near 3.5 keV was recently detected in stacked observations of galaxy clusters and in the Andromeda galaxy (Bulbul et al., 2014a; Boyarsky et al., 2014, Bul14a and Bo14 hereafter). The interpretation of this signal as arising from decaying dark matter, has drawn considerable attention from astrophysics and particle physics communities. The line is also detected in the Suzaku and NuSTAR observations of the core of the Perseus and the Bullet clusters (Wik et al., 2014; Urban et al., 2015; Franse et al., 2016) and in the Galactic center (Boyarsky et al., 2015). An emission line at a consistent energy is also detected in XMM-Newton observations of the Galactic center and in other individual clusters (Iakubovskyi et al., 2015). Recently, a 11$\sigma$-detection of the line was reported in summed NuSTAR observations of the COSMOS and Extended Chandra Deep Field South (ECDFS) survey fields, where a dark matter signal from the Milky-Way halo may be expected (Neronov et al., 2016). As noted, another interesting dark matter candidate that might also produce a 3.5 keV X-ray line is self interacting dark matter from relatively low mass axion-like particles (e.g., Conlon & Day, 2014).

Although the line was detected by several X-ray satellites, including XMM-Newton, Chandra, Suzaku, and NuSTAR in a variety of dark matter-dominated objects, several other studies report non-detections of the line, e.g. in stacked Suzaku observations of clusters of galaxies (Bulbul et al., 2016b), the dwarf galaxy Draco (Ruchayskiy et al., 2016), and Hitomi observations of the Perseus cluster (Hitomi Collaboration et al., 2016). However, the upper limits derived from the stacked galaxies are in tension with the original detection at the $5\sigma$ level (Anderson et al., 2015).

Despite these intensive and persistent efforts, the origin of the 3.5 keV line remains unclear. Potential astrophysical interpretations were discussed extensively by Bul14. A more recent update is provided by Franse et al. (2016), who consider an additional model that comprises a charge exchange between bare Sulfur ions and neutral gas (e.g., Bul14a, Gu et al. 2016, Shah et al. 2016). The radial distribution of the flux of the line can provide an independent test of its origin; however, the observed line flux from the Perseus core is consistent with a dark matter origin (Franse et al., 2016). However, the intensity of the signal in the cluster core appears to be anomalously high for the decaying dark matter model (Bul14a, Franse et al. 2016). In their recent paper, the Hitomi collaboration measure the K XVIII abundance for the first time as 0.6Z*⊙*, well within the allowed limits in Bul14 in the core of the Perseus cluster (Hitomi Collaboration et al., 2016). The other possible astrophysical line which was suggested as a contaminant is Ar XVII DR from lab studies of Electron Beam Ion Trapping measurements (Bulbul et al., 2017). These results have eliminated K XVIII and Ar XVII DR lines as the possible origin for the 3.5 keV line. The $Hitomi$ collaboration reports tension between the flux in the Perseus cluster observed by XMM-Newton and Hitomi at the 3$\sigma$ level. The authors attribute this discrepancy to subtle instrumental features in earlier observations of Hitomi.

Here, we report the detection of the line at $\sim$3.5 keV in the summed data from deep Chandra blank fields, the Chandra Deep Field South (CDFS) and COSMOS for a total exposure of 9.17  Ms. We critically discuss instrumental effects together with four plausible explanations for the origin of the 3.5 keV line – charge exchange; the iron line background; a statistical fluctuation and dark matter decay. All errors quoted throughout the paper correspond to 68% single-parameter confidence intervals. Throughout our analysis we use a standard $\Lambda$CDM cosmology adopting the following values for the relevant parameters: $H_{0}$ =71 km s*-1* Mpc*-1*, $\Omega_{M}=0.27$, and $\Omega_{\Lambda}=0.73$.

2. Data sets

The Chandra-COSMOS Legacy Survey (hereafter, CCLS; Scoville et al., 2007; Elvis et al., 2009; Civano et al., 2016) and the Chandra-Deep Field South (hereafter CDFS; Giacconi et al., 2002; Luo et al., 2008; Xue et al., 2011; Luo et al., 2016) have been observed for $\sim$4.6 M and $\sim$7 Ms respectively, with the ACIS-I CCD instrument onboard Chandra with 117, and 111 pointings, respectively. The CCLS field is a relatively shallow mosaic of $\sim$2 deg2 and an average exposure of $\sim$160 ks/pix while, the CDFS field is a deep pencil beam survey of $\sim$0.1 deg2 observed for 7 Ms/pix. However, since the signal is very faint, for spectral analysis we have only used the pointings observed in the VFAINT telemetry mode with a focal plane temperature of 153.5 K, in order to minimize the instrumental background. Since the CDFS was partly observed in the early phase of the mission when the VFAINT mode wasn’t available and observations were partly taken at higher temperature, the total exposure time before treatment is $\sim$6 Ms.

3. Data Analysis

Raw event files were calibrated using the CIAO tool $chandra\_repro$ and the Calibration Data Base (CALDB) version 4.8. For every pointing, time intervals with high background were cleaned using the CIAO tool $deflare$ using the $lc\_clean$ technique as described by Hickox & Markevitch (2006). The de-flaring was performed in the [2.3-7] keV, [9.5-12] keV and [0.3-3] keV energy band in sequence, in order to detect flares with anomalous hardness ratios (Hickox & Markevitch, 2006). Although not critical for this work, the astrometry was aligned using reference optical catalogs.

The X-ray signal is a blend of detected and unresolved AGN, galaxies and clusters whose summed emission is often referred to as the ”Cosmic X-ray Background” (CXB). There is also a particle-induced background and a (relatively small ) background from other sources within the instrument. Hereafter we will use the acronym CXB for the signal produced by all astrophysical sources that is focused by the optics and we adopt the acronym PIB for the ”Particle and Instrumental Background ” which is produced by all other (non-astrophysical) sources.

For sake of clarity, in this paper, the putative 3.5 keV signal arising either from dark matter decay or Sulfur charge exchange, will be considered as a separate component on top of the CXB and PIB signal. Therefore, we start the analysis by carefully accounting for known X-ray sources, that constitute the PIB and the CXB.

3.1. Extraction of Summed X-ray Spectrum

The detected intensity of the CXB is not the same across the surveys presented here, primarily due to cosmic variance, so we derive an indipendent spectrum for each survey field. For each pointing, we extracted the spectrum of all the photons detected in the ACIS-I field of view (FOV) with the CIAO tool $specextract$. For each spectrum, we then computed the field-averaged Redistribution Matrix Functions (RMFs) and Ancillary Response Functions (ARF) using the CIAO-tool $specextract$. Spectra were co-added and response matrices averaged after weighting by the exposure time. We produced a cumulative CXB+PIB spectrum for each of the datasets. Because we are looking for diffuse emission, the only background component in our observations is the PIB. The Chandra X-ray observatory periodically obtains ”dark frames”, i.e. exposures with ACIS in the stowed mode. When the High Resolution Camera is on the focal plane, ACIS is stowed and unexposed to any focused source but it still records the PIB component. In such a position the ACIS detectors see neither the sky nor the calibration sources. In particular, Hickox & Markevitch (2006) demonstrated that the [2-7] keV to [9.5-12] keV hardness ratio is constant (within 2%) in time regardless of the amplitude of the particle background. Therefore, we employed ACIS-I observations in the stowed mode to evaluate the background. In particular, we merged the $stowed$ mode event files, applied the VFAINT filtering and reprojected to the same astrometric frame as the observations, We then extracted the spectrum in the same source-masked regions and renormalized it by the ratio of count rate in energy bins C*[9.5-12],obs*/C*[9.5-12],stow* where C*[9.5-12],obs* and C*[9.5-12],stow*. In a recent paper, Bartalucci et al. (2014) performed a detailed and sophisticated analysis of the same stowed ACIS-I event files employed here and reported, to within 2%, the relative stability of the background in observations of later epochs than those used by (Hickox & Markevitch, 2006). In this paper, we are looking methodically for astrophysical emission lines in the energy range [2.4-7] keV. In this energy band, the PIB is affected by a systematic uncertainty of the order of 2% which is added in quadrature to the PIB spectral data error bars throughout our analysis. In Table 1, we summarize the number of net counts used for the spectral modeling and the resulting vignetting-weighted final exposures for our datasets. However, we note that the observations in the stowed mode are much shorter than the those employed here (a total of 1 Ms in the archive vs 9.16 Ms). This of course, significantly limits our sensitivity, since the PIB spectrum has larger errors than those in the data and therefore might potentially artificially smooth out any features in the data.

3.2. About the spectrum of PIB

Part of the signal included in the total X-ray spectrum is due to the PIB. In order to find faint sources and/or to analyze faint, diffuse emission-lines, careful treatment of these backgrounds is essential. We start by examining data from ACIS-I in stowed mode, i.e., when no cosmic photons are collected. This provides a robust representation of the particle background plus internal instrumental background. Although an universal model of the PIB is not provided by the Chandra team, here we can model the PIB using a broken power-law, with the slopes ($\Gamma_{PIB,1}$, $\Gamma_{PIB,2}$); the break energy (Ebreak) and the normalization ($norm$) as free parameters. On top of this, we add a Gaussian model at $E\sim 2.5$ keV and $E\sim$5.9 keV, with energies and intensities (I1,2) that are free to vary. The line at 5.9 keV is a known Mn Kα instrumental feature. This feature is scattered light from the radioactive 55Fe in the external calibration source. This source has a half-life of $\sim$2.7 years, so its intensity has dropped dramatically over the course of the Chandra mission. So its not surprising that it (and its K-escape and Ti line) is not fully subtracted from the CXB spectrum. The line at 2.51 keV is instrumental and an artifact: Bartalucci et al. (2014) pointed out that in the [2-3] keV energy band, due the position dependent charge transfer inefficiency (CTI) correction the strong broad emission line at $\sim$2.1 keV ($mother~{}line$) produces a system of spurious $daughter~{}lines$ at energies of up to $\sim$2.6 keV along with spurious broadening. A similar effect is observed above 7.3 keV as well. CTI correction is necessary because radiation has damaged the ACIS-I resulting in loss in the charge transfer inefficiency. This damage however did not affect areas of the CCD not exposed to the X-rays such as the frame store area. To cope with the CTI, a correction is applied $a~{}posteriori$ by the data analysis pipeline. This correction is applied to all the data including those collected by areas not damaged by radiation. The result is that for the strongest instrumental emission lines, the recorded energy is artificially shifted up to 800 eV higher energy (depending on the position on the detector). Detailed modeling of PIB is beyond the scope of this paper an we refer the readers to the Chandra Calibration Database and to specific papers (see e.g. Bartalucci et al., 2014).

4. Results

As noted in Table 1 the spectra analyzed in this paper are background dominated, and this might raise concern when looking for faint emission lines. In this section, we present two different approaches to present the results based on two indipendent methods to handle the background. In the first we subtract the properly normalized PIB spectra from the data and fit and in the second, we fit the CXB+PIB at the same time with models for each component. If we detected the 3.5 keV line if its diffuse coming from the entire of view, we performed the fit using data accumulated over the whole detector and after masking the detected sources.

4.1. Fitting the Background Subtracted Full Spectra Including Point Sources

XSPEC v12.9.0 was used to perform the spectral fits with $\chi^{2}$ as an estimator of the goodness-of-fit. The spectral counts in each energy bin are sufficient to allow the use of the Gaussian statistics in this analysis (Protassov et al., 2002). To increase the sensitivity to weak emission lines, we simultaneously fit the CXB spectra from the CCLS and CDFS. We restrict the energy range to 2.4–7 keV in order to avoid the bright $Au$ feature at 2 keV, while having sufficient leverage on the power-law component. The Galactic column densities are fixed to 2.5$\times 10^{20}$ cm*-2* for the fits of the CCLS field and 8.8$\times 10^{19}$ cm*-2* for the CDFS field (Dickey & Lockman, 1990). The power-law indices and the normalizations are left free in our fits to account for the different CXB flux in the two fields (Hickox & Markevitch, 2006). We first fit the spectra with a single absorbed ($wabs$ model in XSPEC) power-law model which gives an overall good fit with $\chi^{2}$ of 563.43 for 308 degrees-of-freedom (dof).

The best-fit power-law normalizations are found to be: $\sim$2.78 $\times 10^{-4}$ ph keV*-1* cm*-2* s*-1* in CDFS and 2.80$\times 10^{-4}$ ph keV*-1* cm*-2* s*-1* in CCLS. The power-law indices are $\Gamma_{1}$=1.82$\pm{0.10}$ and $\Gamma_{2}$=1.48$\pm{0.06}$ for the two fields, respectively (hereafter the subscripts 1,2 will refer to CDFS and CCLS respectively). The fluxes and spectral indices measured here are in agreement with Hickox & Markevitch (2006), Moretti et al. (2012), Bartalucci et al. (2014) and Cappelluti et al. (2017).

A few spectral features are immediately visible around 2.51 keV, 3.15 keV, 3.5 keV, 4.4 keV, and 6.4 keV. The 2.51 keV line is a strong $Au$-M complex line. We tried to fit the feature at 3.15 keV and didn’t find a significant line but only found a 3$\sigma$ upper-limit of $\sim$1.5$\times 10^{-6}$ ph keV*-1* cm*-2* s*-1*, this means that the feature is just a statistical fluctuation in a few channels. The emission line at 4.37 keV is consistent with a residual from a blend of known instrumental emission lines from Silicon escape (i.e. lines formed by electron clouds left when a photon carrying away energy leaves silicon substrate)111http://cxc.harvard.edu/cal/Acis/Cal_prods/matrix/notes/Fl-esc.html from Mn K${}_{\alpha_{1,2}}$ and Ti K${}_{\alpha_{1,2}}$ 222http://www2.astro.psu.edu/xray/docs/cal_report/node155.html given that the energy resolution is $>$200 eV at these energies. These two weak emission lines are hard to detect in the PIB due to limited statistics but they become clearly visible in the deep blank-sky observations used here or can be produced by a minimal leaking of the on board calibration source. The line at 6.4 keV is consistent with Fe Kα and for this line we cannot discriminate between an instrumental or a Galactic origin. Adding the Gaussian components for the instrumental lines at 2.51 keV, 3.15 keV, 4.4 keV, and 6.4 keV with variable energies and normalizations improves the $\chi^{2}$ value by a significant amount with $\chi^{2}$ of 527.01 for 298 dof.