Technical comment on the paper of Dessert et al.
“The dark matter interpretation of the 3.5 keV line is inconsistent with
blank-sky observations”

Alexey Boyarsky1, Denys Malyshev2, Oleg Ruchayskiy3, Denys Savchenko4,5*

1 Lorentz Institute, Leiden University,

Niels Bohrweg 2, Leiden, NL-2333 CA, The Netherlands

2 Institut für Astronomie und Astrophysik Tübingen,

Universität Tübingen, Sand 1, D-72076 Tübingen, Germany

3 Niels Bohr Institute, Copenhagen University,

Blegdamsvej 17, Copenhagen, DK-2100, Denmark

4 Bogolyubov Institute for Theoretical Physics,

Metrolohichna Str. 14-b, 03143, Kyiv, Ukraine

5 Kyiv Academic University, 36 Vernadsky blvd., Kyiv, 03142, Ukraine

*<EMAIL_ADDRESS>
## Abstract

An unidentified line at energy around 3.5 keV was detected in the spectra of
dark matter-dominated objects. Recent work [1] used 30 Msec of XMM-Newton
blank-sky observations to constrain the admissible line flux, challenging its
dark matter decay origin. We demonstrate that these bounds are overestimated
by more than an order of magnitude due to improper background modeling.
Therefore the dark matter interpretation of the 3.5 keV signal remains viable.

An X-ray line at $E\simeq 3.5$ keV has been found in 2014 [2, 3]. Many
consistency checks, as well as follow-up detections, have been reported, while
non-detections have not ruled out the dark matter interpretation of the signal
(see [4] for review). Ref. [1] (DRS20 in what follows) recently reported
bounds on the decay lifetime, which are about an order of magnitude below
those required for dark matter interpretation. The improvements of these
bounds compared with the previous results are much stronger than one would
expect based solely on the increase of the exposition. We demonstrate that
such a strong increase is mainly an artifact of overly restrictive background
modeling.

Figure 1: Upper limits (95% CL) on the extra line flux against the models, described in Table 1 (colors coincide with the model names). Data points show the energies where the lines are detected at more than $3\sigma$ level over the continuum of the corresponding color (errorbars are $\pm 1\sigma$). Figure 2: Shown are the actual spectra and background models, described in this Comment. The necessity for the additional astrophysical lines above the continuum powerlaw is clearly seen. One can see that the level of the background continuum decreases with the addition of astrophysical lines. The dashed magenta line shows the model with the line at $E_{\text{fid}}$ included. Vertical dashed lines correspond to the modeling range of “blue”, “green”, and “red” models. Model |  Model | Interval |  $\chi^{2}$/dof | Line at |  $95\%$CL at $E_{\rm fid}$
---|---|---|---|---|---
name |  components |  |  |  $E_{\rm fid}$? |  $10^{-6}$ cm-2s-1
Blue |  Powerlaw | 3.3-3.8 keV | 88.76/96 | No | 0.16
Green |  Powerlaw
Line @ 3.3 keV
Line @ 3.68 keV | 3.3-3.8 keV | 68.86/96 | No ($0.8\sigma$) | 0.70
Red |  Powerlaw
Line @ 3.3 keV
Line @ 3.68 keV | 3.3-3.8 keV | 68.86/94 | No ($1.3\sigma$) | 1.41
Magenta |  Powerlaw
Line @ 3.12 keV
Line @ 3.3 keV
Line @ 3.68 keV
Line @ 3.9 keV | 3.0-4.0 keV | 163.0/193 | Yes ($4.0\sigma$) | 1.72
Table 1: Four background models for line search.

We use $17$ Msec of _XMM-Newton_ MOS observations pointing
$20^{\circ}-35^{\circ}$ off the Galactic Center.111For the list of
observations see [5].  This dataset contains 57% of the total exposure of
DRS20, including 503 of their 534 observations. Thus, we expect the flux upper
limit to differ by $\approx\sqrt{30/17}\approx 1.32$. Different dark matter
profiles are consistent with each other in this region making the limits more
robust.

Our results are shown in Fig. 1, while Table 1 summarizes the details of our
modeling and shows 95% CL at fiducial energy $E_{\rm fid}=3.48$ keV.

First, we searched for a narrow line atop of a folded powerlaw (plus an
instrumental continuum fixed at high energies) across the interval 3.3-3.8
keV. Our limits (“blue model”) are consistent with DSR20: strong constraints
around $3.5$ keV, lines at $\sim 3.3$ and $3.68$ keV detected with
significance $\geq 3\sigma$, consistently with significant weakening on the
DRS20 limits at these energies. Such lines (Ar XVIII and S XVI complexes
around 3.3 keV, and Ar XVII plus K XIX around 3.68 keV) are detected in
astrophysical plasma both in galaxy clusters [6, 2, 7] and in our Galaxy [8,
9, 10, 11]. Besides, the presence of the weak instrumental lines – K K$\alpha$
at 3.3 keV and Ca K$\alpha$ at 3.7 keV has been reported, see [11] and refs.
therein.

Therefore, next we add to the model extra Gaussians at 3.3 keV and 3.68 keV
(“green model”, Table 1) and repeat the analysis in the 3.3-3.8 energy range.
The bounds weaken by a factor $\sim 4$ (Fig. 1, green line) at $E_{\rm fid}$.
This weakening is consistent with Fig. S14(A) of DRS20. A background model
without these lines raises the powerlaw continuum, which artificially lowers
the upper limit on any line (see [12] for the previous discussion). Indeed,
Fig. S16(B) of DRS20 demonstrates that the bestfit value of the line flux at
$3.5$ keV, parametrized by $\sin^{2}(2\theta)$, is negative at the level
$\sim-1.5\sigma$ – background is over-subtracted. We notice that the
normalization of two lines at the end of the interval was fixed to their best-
fit value during this procedure.

When, instead, we let the normalization of the lines vary freely, while adding
an extra line around $3.5$ keV (as in [2, 3, 9, 12]) – the upper limit on the
flux weakened by an extra factor of $\sim 2$ (“red model”).

Interval 3–4 keV contains two more known lines – Ca XIX complex around $3.9$
keV and Ar XVII plus S XVI around $3.1$ keV c.f. [2, 9, 11]. We repeat our
analysis in this interval with two extra lines in the model (“magenta model”).
We find a $4\sigma$ line at $E_{\rm fid}$ and the upper limit weakens
accordingly. Further extending the model to 2.8–6.0 keV, carefully modeling
all astrophysical and instrumental lines and accounting for all significant
line-like residuals, does not change the results.

The described above models are shown in 3 – 4 keV energy band in Fig. 2 with
corresponding colours. Fig. 2 illustrates that the model with no astrophysical
lines fails to adequately model the data on a broader energy range, and
overestimates the continuum level, as discussed above.

## Conclusion

We demonstrate that the constraints from long exposure blank-sky observations
[1] strongly depend on the background model. Namely, proper inclusion of the
line complexes at 3.3 keV and 3.68 keV relaxes the bound by a factor $\sim 8$.
The extension of the fitting interval to 3–4 keV weakens the bound by more
than an order of magnitude (magenta line in Fig. 1 compared to the blue line,
reproducing DRS20) and also leads to the detection of the line at 3.5 keV at
$4\sigma$.

DRS20 investigates the effects of these lines in the Supplementary Material.
However they (i) fix normalization of their best fit background values,
reducing their effect (reproduced by our “green” model) and (ii) chose to
report more stringent bounds as their final result.

When claiming _exclusions_ , one should be careful to push all systematic
uncertainties in the conservative directions. In this particular case, to
claim the strongest “powerlaw” bound (as done in DRS20) one should _prove_
that other known lines are not present in a particular dataset. Moreover, if
the analysis at a wider energy interval (3–4 keV) gives weaker constraint, we
see no reason not to report it as a proper conservative bound.

Furthermore, to interpret the exclusion in terms of the decaying dark matter
lifetime, one needs to adopt the most conservative density profile. In
particular, the local dark matter density was adopted in DRS20 to be
$0.4\,\mathrm{GeV/cm^{3}}$. It has a systematic uncertainty of a factor $2-3$
[13], see also discussion in [14], which should be propagated into the final
conservative bound.

The spectral resolution of modern X-ray satellites is below that, required to
resolve the intrinsic shape of astrophysical or putative dark matter decay
lines. Future X-ray spectrometers will be able to finally settle this
question.

## Other comments

Below we comment on other inconsistencies in DRS20. The above conclusions are
not based on them.

### PN out-of-time events not subtracted?

For the PN camera the out-of-time events were not subtracted. Indeed, the
scripts dl2dat.sh and spc2dat.py of DRS20 show that count rates from files
pn*-obj.pi, produced by the ESAS script pn-spectra were used. Instead, out-of-
time subtracted spectra, produced by pn_back (filename pattern pn*-obj-os.pi)
should have been used, according to the ESAS manual.

### Wrong PN count rate?

Fig. 2 of DRS20 shows that counts rates of stacked MOS and PN spectra are
similar. However, it is known that count rate of the PN camera is $\approx 3$
times higher than of the MOS cameras, c.f. [15, Fig. 7 & Table 2] or [12, Fig.
1]. This difference is not explained in the text. DSR20 showed the count rate
for the PN camera of ObsID 0653550301 (Fig. S11) which we reproduced. The MOS
count rate for the same observation is a factor of $\sim 3$ lower.

### Acknowledgements.

The authors acknowledge communication with K. N. Abazajian and D. Iakubovskyi.
This project received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (GA
694896) (AB and OR). The work of DM was supported by DFG through the grant MA
7807/2-1. OR acknowledges support from the Carlsberg Foundation. The authors
acknowledge support by the state of Baden-Württemberg through bwHPC.

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