Starburst Nuclei as Light Dark Matter Laboratories Antonio Ambrosone1 2Marco Chianese1 2Damiano F.G. Fiorillo3Antonio Marinelli1 2 4 and Gennaro Miele1 2 5

2025-04-24 0 0 1013.5KB 17 页 10玖币

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Starburst Nuclei as Light Dark Matter Laboratories

Antonio Ambrosone,1, 2, ∗Marco Chianese,1, 2, †Damiano F.G.

Fiorillo,3, ‡Antonio Marinelli,1, 2, 4, §and Gennaro Miele1, 2, 5, ¶

1Dipartimento di Fisica “Ettore Pancini”, Universit`a degli studi di Napoli

“Federico II”, Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy

2INFN - Sezione di Napoli, Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy

3Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

4INAF-Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131 Naples, Italy

5Scuola Superiore Meridionale, Universit`a degli studi di Napoli “Federico II”, Largo San Marcellino 10, 80138 Napoli, Italy

(Dated: September 18, 2023)

Starburst galaxies are well-motivated astrophysical emitters of high-energy gamma-rays. They

are well-known cosmic-ray “reservoirs”, thanks to their large magnetic ﬁelds which conﬁne high-

energy protons for ∼105years. Over such long times, cosmic-ray transport can be signiﬁcantly

aﬀected by scatterings with sub-GeV dark matter. Here we point out that this scattering distorts

the cosmic-ray spectrum, and the distortion can be indirectly observed by measuring the gamma-

rays produced by cosmic-rays via hadronic collisions. Present gamma-ray data show no sign of such

a distortion, leading to stringent bounds on the cross section between protons and dark matter.

These are highly complementary with current bounds and have large room for improvement with

the future gamma-ray measurements in the 0.1–10 TeV range from the Cherenkov Telescope Array,

which can strengthen the limits by as much as two orders of magnitude.

Introduction. — The existence of Dark Matter (DM)

is a milestone of the cosmological standard model [1].

However, its nature has not been identiﬁed yet [2–5].

Astrophysical and cosmological observations reveal that

galaxies, including the Milky Way (MW), posses a halo

of non-relativistic DM particles [6–10]. This has allowed

direct-detection experiments to place powerful limits on

the properties of DM particles which may elastically scat-

ter oﬀ target nuclei [5]. However, due to poor sensitiv-

ity at low nuclear recoil energies, such searches are typ-

ically limited to DM masses higher than 1 GeV, leav-

ing sub-GeV DM largely unexplored by direct measure-

ments. To probe such light DM particles, novel ap-

proaches are required in addition to standard astrophys-

ical [6,7,11–14], cosmological[15–20], and collider [21]

searches. Ref. [22] proposed one such approach, point-

ing out that the spectrum of MW Cosmic-Rays (CRs)

can be altered by DM-CR elastic interactions. Soon af-

ter, Refs. [23,24] showed that this interaction produces

Boosted Dark Matter (BDM) particles, which can then

be probed in direct-detection experiments due to their

large energies (see Refs. [25–51] for other BDM studies).

Up until now, the impact of DM-CR interaction has

been mainly analyzed in the context of our own Galaxy

(few exceptions are Ref. [26,52–54]). However, CRs suf-

fer a larger eﬀect in environments which conﬁne CRs for

long times, so that they traverse through the DM halo

longer. Therefore, in this Letter we propose to use cosmic

reservoirs, namely sources which conﬁne cosmic-rays, as

∗aambrosone@na.infn.it

†chianese@na.infn.it

‡damiano.ﬁorillo@nbi.ku.dk

§antonio.marinelli@na.infn.it

¶miele@na.infn.it

a probe of DM-CR interactions. We focus on the nu-

clei of starburst galaxies (hereafter denoted as SBNi),

which conﬁne CRs [55–57] for ∼105years even at en-

ergies as large as 100 TeV. While these CRs cannot be

directly observed, they produce gamma-rays and neutri-

nos via hadronic collisions [55–61]. Therefore, DM-CR

interaction can distort the CR spectrum, and in turn the

gamma-ray ﬂux observed from SBNi (see Fig. 1). Here

we show that the gamma-ray data from two nearby star-

burst galaxies, M82 and NGC 253, do not exhibit such

a distortion, allowing us to bound the DM-CR cross sec-

tion at the level of 10−34 cm2for DM with 10 keV masses,

as shown in Fig. 2. The bounds can be substantially im-

proved with a better knowledge of the gamma-ray ﬂux at

energies 0.1–10 TeV. We show that the future Cherenkov

Telescope Array (CTA) [62] will be able to strengthen

these bounds by as much as two orders of magnitude.

Cosmic-Ray transport in SBNi. — High-energy

gamma-rays in SBNi are produced by CRs, here assumed

to be injected by supernova remnants. CR protons collide

with interstellar gas, hadronically producing π0which de-

cay to gamma-rays, while CR electrons leptonically pro-

duce gamma-rays via bremsstrahlung and inverse Comp-

ton scattering. Following Refs. [55,56], we assume steady

balance between CR injection and cooling, advective, and

diﬀusive escape from the SBN, modeled as a compact

sphere with radius RSBN ∼102pc. The CR momentum

distribution fCR(p) is

fCR(p) = 1

τadv

τdiﬀ

τeﬀ

loss −1

QCR(p),(1)

where QCR(p) is the injection rate from supernova rem-

nants, and τiare the timescales for the various processes.

We assume injection of primary protons and electrons

with a power-law spectrum of spectral index Γ + 2, as

arXiv:2210.05685v2 [astro-ph.HE] 15 Sep 2023

expected from diﬀusive shock acceleration. In principle,

there might be a contamination of heavier nuclei e.g. He-

lium nuclei (see the Supplemental Material VI, which in-

cludes Refs. [63–68]) We also assume the injection rates

to be directly proportional to the star formation rate of

the source ˙

M∗. Nevertheless, our results are independent

of the speciﬁc acceleration mechanism, provided that the

cosmic-rays follow a power law. We introduce an ex-

ponential cut-oﬀ at 10 PeV for protons and a gaussian

cut-oﬀ at 10 TeV for electrons. The advection timescale

is τadv =RSBN/vwind, where vwind is the wind velocity.

Even though, for these sources, diﬀusion is expected to

be irrelevant below 1 PeV [69–71], we introduce it ac-

cording to Ref. [55]. Finally, the energy-loss timescale

τeﬀ

loss =1

Γ−1"X

i−1

dti#−1

,(2)

where the sum comprises radiative and collision pro-

cesses (for further details see the Supplemental Mate-

rial I, which includes Refs. [72,73]). In Eq. (2), we con-

sider for protons ionization, Coulomb interactions, and

proton-proton collisions, while for electrons ionization,

synchrotron, bremsstrahlung, and inverse Compton scat-

terings oﬀ low-energy photons. From the CR distribu-

tion in Eq. (1), we obtain the gamma-ray spectrum, ac-

counting both for pion production from proton-proton

collisions and its subsequent decay, and for primary and

secondary bremsstrahlung and Inverse Compton scatter-

ing (for further details see the Supplemental Material II,

which includes Refs. [74,75]).

DM-proton scatterings inside SBNi. — If nucle-

ons are coupled to DM (hereafter called χ), CRs conﬁned

in the SBN are trapped for such a long time that they

can collide with DM. Elastic DM-CR scatterings cause

an additional energy-loss in Eq. (2), competing with the

others for suﬃciently large DM-proton cross sections:

τel

χp ="−1

EdE

dtχp#−1

,(3)

with

dE

dtχp

=ρχ

mχZTmax

dTχTχ

dσel

dTχ

,(4)

where mχis the DM mass, ρχis the spherically-

symmetric DM density within the SBN, and dσel/dTχ

is the diﬀerential elastic DM-proton cross section as a

function of the ﬁnal DM kinetic energy Tχ. The maxi-

mal allowed value Tmax

χfor Tχin a collision with a proton

with kinetic energy T=E−mpis

Tmax

χ=2T2+ 4mpT

mχ"1 + mp

mχ2

+2T

mχ#−1

.(5)

The diﬀerential cross section depends on the DM-proton

interaction. For deﬁniteness, we consider Dirac fermion

DM particles interacting with protons via a scalar media-

tor with a mass much larger than the transfer momentum

q2= 2mχTχ. Diﬀerently from Refs. [22,26], that assume

a constant cross section with a ﬂat spectrum in recoil

energy, for Tχ≤Tmax

χwe have [25]

dσel

dTχ

=σχp

Tmax

p(q2)

16 µ2

χp s(q2+ 4m2

p)(q2+ 4m2

χ),(6)

where σχp is the DM-proton cross section at zero center-

of-mass momentum, µχp is the reduced mass of χand

proton, and s=m2

χ+m2

p+ 2Emχis center-of-mass en-

ergy. The quantity Fpis the proton form factor [76]

Fp(q2) = 1

1 + q2/Λ22

with Λ = 0.770 GeV .(7)

At energies much higher than m2

p/2mχ, DM-CR scatter-

ings become inelastic, breaking the proton and produc-

ing additional gamma-rays from the pion decay [77]. We

model this process via a simple semi-analytic approxima-

tion similar to Refs. [39,78,79]: we assume the DM-CR

inelastic cross section to follow the neutrino-nucleon one

and rescale it to match the DM-CR cross section in the

elastic regime. In this way, the inelastic cross section

(σinel) is totally deﬁned by means of σχp in Eq. (S18).

The timescale for energy loss from inelastic DM-CR col-

lision is

τinel

χp =κ σinel

ρχ

mχ−1

,(8)

where κis the inelasticity of the process, assumed to

be 0.5 as for inelastic proton-proton collisions. Finally,

to evaluate the gamma-ray production in inelastic DM-

CR scattering, we assume from each collision a gamma-

ray emissivity analogous to proton-proton collision (for

details see the Supplemental Material II).

The DM-CR scattering rate depends on the DM den-

sity distribution, which is pretty uncertain in the central

cores of galaxies [82–84]. A benchmark parameterization

is the Navarro-Frenk-White (NFW) distribution [85]

ρχ(r) = ρs

r/rs(1 + r/rs)2(9)

which is a function of the radial distance rfrom the SBN

center. The scale radius rsand the normalization ρs

can be expressed through the concentration parameter

c200 =r200/rsand the mass M200 enclosed in a sphere

of radius r200, which is deﬁned as the distance at which

the mean DM density is 200 times the critical Universe

density ρc. These parameters are not measured, so we use

the results of the simulations in Refs. [9,10,86], showing

that 7 ≤c200 ≤12 and 1010 ≤M200/M⊙≤1012. As

benchmark cases in the following analysis we use c200 = 7

for both sources, M200 = 1012 M⊙for M82 and M200 =

3×1011 M⊙for NGC 253 [9,10,86]. In the Supplemental

Material IV (which includes Refs. [87,88]) we quantify

10−1100101102103104105106

Proton kinetic energy, T[GeV]

102

103

104

105

106

107

Timescales, τ[yr]

Standard losses

Advection

Diﬀusion

M82

χp elastic

χp inelastic

Case 1: mχ= 10−1GeV, σχp = 10−25 cm2

Case 2: mχ= 10−3GeV, σχp = 10−29 cm2

Case 3: mχ= 10−5GeV, σχp = 10−34 cm2

10−1100101102103104105

Gamma-ray energy, Eγ[GeV]

10−11

10−10

10−9

SED, E2

γΦγ[GeV cm−2s−1]

M82

Standard emission

Case 1

Case 2

Case 3

CTA sensititivy

Current data

FIG. 1. Left panel. Comparison between the proton timescales within M82 as a function of the proton kinetic energy T. The

continuous, dashed and dotted black lines represent the standard losses, advection and diﬀusion timescales, respectively. The

colored continuous (dashed) lines correspond to the elastic (inelastic) DM interactions for three diﬀerent cases. Right panel.

The expected gamma-ray ﬂuxes from M82 compared to current data [80,81] and CTA sensitivity [62]. Analogously to the left

panel, the black color line corresponds to the standard case (without DM-CR interactions), while the colored lines to the three

diﬀerent choices of (mχ, σχp ).

the impact of varying the halo parameters in the expected

range, showing that it leads to an uncertainty of at most

one order of magnitude in the constraints on DM-proton

cross section σχp.

Observable features in the gamma-ray spec-

trum. — The additional energy loss from elastic DM-CR

interactions cause a suppression in the CR, and therefore

in the gamma-ray spectrum, whereas the inelastic DM-

CR production can replenish the gamma-ray spectrum at

higher energies. These eﬀects are visible in Fig. 1which

represents the case of M82 source. The left panel shows

the DM-CR energy-loss timescales (τel

χp and τinel

χp ), av-

eraged within the SBN volume, in comparison with the

standard timescales. At low CR energies, T≪Ep

dip =

p/(2mχ), τel

χp ≃3m4

p/2ρχσχpT3rapidly decreases with

the CR kinetic energy. At high CR energies, elastic scat-

tering becomes progressively unlikely compared with the

inelastic one, so τel

χp ≃128m6

χT3/ρχσχpΛ8lnT mχ/2m2

p

increases with the CR kinetic energy. Elastic DM-CR

scattering thus can cause a dip in the CR spectrum

at an energy Ep

dip ≃m2

p/2mχ, due to protons being

pushed to lower energies. Above the dip, inelastic DM-

CR scattering becomes the dominant source of CR energy

loss. In each scattering the CR energy is reprocessed

in gamma-rays, leading to a new calorimetric regime in

which the gamma-ray spectrum again follows the CR in-

jection power-law spectrum.

The right panel of Fig. 1shows the resulting gamma-

ray spectrum, evidencing the dips corresponding to dif-

ferent masses mχdue to elastic DM-CR scattering at an

energy Eγ

dip ≃0.1Ep

dip – since gamma-rays carry on aver-

age 10% of the parent CR energy – and the higher-energy

power-law behavior of the gamma-rays from inelastic

DM-CR scattering. The latter can exceed the gamma-

rays produced in the standard proton-proton dominated

regime (black line), in which the calorimetry is partial

due to competition with advective escape. In the stan-

dard case without DM-CR interactions, only a fraction

τeﬀ

loss/(τeﬀ

loss +τadv)∼40% of the protons lose all of their

energy to gamma-rays. However, we emphasize that the

normalization of the gamma-ray spectrum after the dip

also depends on the assumed inelasticity, which by rigor

should be determined from the speciﬁc DM-quark cou-

pling. Nevertheless, this has no signiﬁcant impact on the

bounds we derive, which essentially depend only on the

behavior in the dip region and therefore on the elastic

DM-CR scattering. Moreover, it is worth noticing that

leptonic processes are completely subdominant in SBNi

and cannot reduce the amplitude of the dip.

Statistical analysis. — We analyze GeV-TeV data

for both M82 and NGC 253. GeV data are obtained

from the 10-year Fermi-LAT observation [81]. TeV data

are taken for M82 from VERITAS [80] and for NGC 253

from H.E.S.S. [89]. All data-sets show a gamma-ray pro-

duction up to TeV, with no hint of a break. Therefore,

they strongly constrain DM-CR interactions.

To obtain these bounds, we follow Refs. [57,61], deﬁn-

ing the likelihood as

L(mχ, σχp, θ) = e−1

2PiSEDi−E2

iΦγ(Ei|mχ,σχp,θ)

σi2

,(10)

where SEDiis the measured spectral energy distribution

data, Eiand σiare respectively the centered energy bin

value and the uncertainty on the data, and iruns over

the number of data points. Finally, Φγ(Ei|mχ, σχp, θ)

is the gamma-ray ﬂux we compute, where θrepresents

the astrophysical nuisance parameters which are: ˙

M∗,

Γ, RSBN,vwind,nISM, with nISM being the interstellar

10−610−510−410−310−210−1100

mχ[GeV]

10−40

10−38

10−36

10−34

10−32

10−30

10−28

10−26

10−24

σχp [cm2]

M82: Fermi + VERITAS

NGC 253: Fermi + H.E.S.S.

+ CTA

MWCR cosmo

Blazar-BDM

MWCR-BDM

colliders

FIG. 2. Constraints at 5σon DM-proton cross section placed

by means of current (thick solid lines) and future CTA (thick

dashed lines) data for M82 (red color) and NGC 253 (yellow

color) galaxies. For comparison, the constraints from cos-

mological observations [20], direct-detection experiments [94–

110], colliders [21], Milky-Way Cosmic-Rays (MWCR) [22],

boosted dark matter from the blazar BL Lac (Blazar-BDM)

with MiniBooNE (cyan dot-dashed lines) and XENON1T

(cyan solid lines) detectors [26], and boosted dark matter

due to MW cosmic-rays scatterings through a heavy medi-

ator (MWCR-BDM) [47] are reported.

gas density (the target for proton-proton collisions). For

each of these parameters, we consider the realistic linear

priors discussed in Ref. [61] to take into account the as-

trophysical uncertainties on the structural properties of

M82 and NGC 253 (see for details Supplemental Mate-

rial III, which includes Refs. [90–93]).

In order to obtain bounds on the DM-CR cross sec-

tion, from the marginalized chi-squared χ2(mχ, σχp) =

−2 ln maxθL(mχ, σχp, θ) we deﬁne the test statistic

∆χ2=χ2(mχ, σχp)−χ2(mχ,0), comparing with the zero

interaction case. We set bounds at 5σconﬁdence level by

requiring ∆χ2= 23.6, since in the hypothesis of a DM

signature the test statistic is distributed as a half-chi-

squared variable.

Results and discussion. — Fig. 2summarizes the

bounds we ﬁnd on σχp as a function of mχ, both for

the case of M82 and NGC 253. The bounds ﬂatten

out for mχ≲1 keV, since lighter masses cause a dip

at Eγ

dip ≳50 TeV, where gamma-rays cannot be ob-

served due to attenuation on extragalactic background

light. NGC 253 leads to signiﬁcantly better bounds at

low masses due to the larger number of data points in the

TeV region. Indeed, the main limitation from present-

day data is the limited statistics in the 1 −10 TeV win-

dow. To quantify this, we perform a forecast analysis for

the CTA telescope [62], for both sources. CTA will dra-

matically improve the gamma-ray measurements in this

energy region, as already shown in Ref. [61]. We generate

50 mock data samples (see the Supplemental Material V

for details), and we obtain the projected bounds for each

sample. Fig. 2shows the mean values of these bounds.

CTA will strengthen the constraints up to two orders of

magnitude for NGC 253 and ﬁve orders of magnitude for

M82 in the low-mass region. We emphasize that con-

straining DM-CR scattering using starburst galaxies has

the additional advantage that diﬀerent galaxies can be

used to make the results more robust, and the bounds

from diﬀerent sources can be combined to provide more

stringent exclusions on the DM properties.

Our bounds are complementary to the direct-detection

of boosted DM, whose bounds exhibit a ceiling due to the

atmosphere attenuation of the BDM ﬂux. Our bounds

also look signiﬁcantly stronger than the ones placed

in Ref. [22] by searching for distortions of the Milky-

Way CR spectrum due to DM-CR scattering, while for

mχ≲1 MeV they are comparable with the ones de-

rived from the non-observation of BDM particles from

DM-CR interactions in blazars [26]. However, the lim-

its [22,26] have been both obtained assuming an energy-

independent DM-CR cross section, whereas we include

the typical σχp ∝E2behavior due to a massive me-

diator, and a ﬂat distribution for the DM recoil en-

ergy. Naively, since our bounds primarily come from CRs

around 10 TeV energies in the low-mass range, whereas

σχp is deﬁned at a center-of-mass energy of order GeVs,

they are stronger than the ones in Ref. [22] by about 108

just because of the diﬀerent cross section behavior. How-

ever, the diﬀerence in the recoil energy distribution also

leads to a completely diﬀerent shape for the bounds. For

this reason, a comprehensive comparison would require a

re-evaluation of their results, which is beyond the scope

of this Letter.

Diﬀerently from the Milky Way [78], in SBNi the in-

elastic DM-CR scatterings are also less observationally

interesting, since they just replace the proton-proton

scatterings in making CRs lose their energy to gamma-

rays. However, bounds based on inelastic scattering in

the Milky Way are strongly dependent on how the diﬀer-

ential cross section for gamma-ray production is modeled,

which in turn requires a speciﬁc choice of the quark-DM

coupling. Furthermore, these bounds are applicable only

at large enough DM masses, in order that the cosmic-

rays exceed the pion production threshold. Our bounds

instead depend essentially on the elastic scattering, which

requires no threshold condition, and therefore are robust

against these uncertainties.

Concerning the blazar-BDM bounds, we also empha-

size that they rely on the existence of a DM spike close

to the central black hole. This is ﬁrst of all impacted by

the possibility of DM annihilation in the spike, as shown

by Ref. [26]. Furthermore, the steepness of the DM pro-

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StarburstNucleiasLightDarkMatterLaboratoriesAntonioAmbrosone,1,2,∗MarcoChianese,1,2,†DamianoF.G.Fiorillo,3,‡AntonioMarinelli,1,2,4,§andGennaroMiele1,2,5,¶1DipartimentodiFisica“EttorePancini”,Universit`adeglistudidiNapoli“FedericoII”,ComplessoUniv.MonteS.Angelo,I-80126Napoli,Italy2INFN-SezionediNapol...

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