Probing the galactic cosmic-ray density with current and ...

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Astronomy & Astrophysics manuscript no. aanda ©ESO 2021 October 19, 2021 Probing the galactic cosmic-ray density with current and future γ-ray instruments G. Peron 1 and F. Aharonian 1,2 1 Max Plank Institute für Kernphysik, P.O. Box 103980, D-69029 Heidelberg, Germany e-mail: [email protected] 2 Dublin Institute for Advanced Studies, 10 Burlington Rd, Dublin, D04 C932, Ireland e-mail: [email protected] Received ; accepted ABSTRACT Context. Cosmic Rays (CRs) propagating through dense molecular clouds (MCs) produce gamma-rays which carry direct information about the CR distribution throughout the Galaxy. Observations of gamma-rays in dierent energy bands allow exploration of the average CR density in the Galactic Disk, the so-called level of the "CR Sea". Fermi-LAT observations have demonstrated the method’s feasibility based on two dozen MCs in our Galaxy. However, the potential of Fermi-LAT is limited by the most massive and relatively nearby MCs; thus, the current observations cover only a tiny fraction of the Milky Way. Aims. In this paper, we study the prospects of expanding the CR measurements to very and ultra-high energies and remote parts of the Galaxy with the current and next-generation detectors. Methods. Based on calculations of fluxes expected from MCs, we formulate the requirements to the sensitivity of the post-Fermi- LAT detectors to map GeV-TeV CRs in the Galactic Disk. We also explore the potential of the current and future air-shower and atmospheric Cherenkov telescope arrays for the extension of CR studies to multi-TeV and PeV energy bands. Results. We demonstrate that the improvement of the Fermi-LAT sensitivity by a factor of a few would allow a dramatic increase in the number of detectable MCs covering almost the entire Galaxy. The recently completed LHAASO should be able to take the first CR probes at PeV energies in the coming five years or so. Key words. cosmic rays, Gamma rays: ISM, ISM:clouds 1. Introduction The paradigm of Galactic cosmic rays (CRs) assumes that the lo- cally measured CR density (ρ (1GeV) 1 eV/cm 3 ), represents the average level of CRs in the Galactic Disk (GD) (see, e.g. Am- ato & Casanova (2021)). During their confinement in the GD, CRs mix and lose track of their production sites, creating the so-called "CR sea". The spatial distribution of CRs in the Milky Way depends on the distributions of CR sources and the diusion coecient characterizing the CR propagation in GD. It is be- lieved that the mixture of CRs caused by diusion is so eective that one should expect uniform distribution of CRs throughout the Galaxy with almost constant level of the "CR sea". However, significant deviations of the density cannot be excluded both on small (tens of parsecs) scales because of the concentration of ac- tive or recent CR accelerators and on large (kiloparsec) scales due to the spatial variations of the CR diusion coecient. The locally measured CR fluxes give direct information about the "CR sea level" only in a single point in the Milky Way. Meanwhile the measurements of the "CR sea" level throughout the Galaxy is of paramount importance. Low-energy (MeV/GeV) CRs play a significant role in the regulation of the ionization, chemistry, and the dynamics of the gas and dust, and consequently on the star and planet formation (Padovani et al. 2020). Moreover, CRs might have a non-negligible impact on the habitability of planets around other stars (Atri et al. 2014). At very high energies, the influence of CRs on these processes is less pronounced. However, the information about the distribu- tion of highest energy CRs in the GD is essential for searching for CR TeVatrons and PeVatrons in the Milky Way. Gamma-ray astronomy provides a unique channel for inves- tigating the distribution of CRs far from the Solar System. Of particular interest is the gamma-ray emission produced at in- teractions of CRs with the interstellar medium (ISM) which provide straightforward information on the CR content at the location of the interaction. The observations with the Fermi- Large Area Telescope (LAT) demonstrated the feasibility of this method: CR densities have been extracted both from studies of the diuse gamma-ray emission emission (Acero et al. 2016; Yang et al. 2016; Pothast et al. 2018) and from giant molecular clouds (GMCs) (Yang et al. 2015; Neronov et al. 2017; Aharo- nian et al. 2020; Peron et al. 2021). The latter, being small re- gions of enhanced gas density, provide localized information on the CR content with accuracy better than 100 pc. Fermi-LAT is the only instrument that succeeded in exten- sively measuring the γ-ray flux from "passive", i.e. a cloud with- out having in the proximity of currently operating CR sources, GMCs. Yet, the detection is limited to exceptionally massive (& 10 6 M ) or nearby (d. 1 kpc) clouds, if the illuminating CR flux coincides with the local flux of cosmic rays, J .The soft power-law spectrum of the "CR sea" (α 2.7) makes the stud- ies at TeV and higher energies very dicult. The HAWC Col- laboration reported upper flux limits from local molecular clouds (Abeysekara et al. 2021) which agree with the above assessment. Meanwhile, the H.E.S.S. Collaboration reported the detection at TeV energies of a GMC located in the galactic plane that shows Article number, page 1 of 9 arXiv:2110.08778v1 [astro-ph.HE] 17 Oct 2021

Transcript of Probing the galactic cosmic-ray density with current and ...

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Astronomy & Astrophysics manuscript no. aanda ©ESO 2021October 19, 2021

Probing the galactic cosmic-ray density with current and futureγ-ray instrumentsG. Peron1 and F. Aharonian1,2

1 Max Plank Institute für Kernphysik, P.O. Box 103980, D-69029 Heidelberg, Germanye-mail: [email protected]

2 Dublin Institute for Advanced Studies, 10 Burlington Rd, Dublin, D04 C932, Irelande-mail: [email protected]

Received ; accepted

ABSTRACT

Context. Cosmic Rays (CRs) propagating through dense molecular clouds (MCs) produce gamma-rays which carry direct informationabout the CR distribution throughout the Galaxy. Observations of gamma-rays in different energy bands allow exploration of theaverage CR density in the Galactic Disk, the so-called level of the "CR Sea". Fermi-LAT observations have demonstrated the method’sfeasibility based on two dozen MCs in our Galaxy. However, the potential of Fermi-LAT is limited by the most massive and relativelynearby MCs; thus, the current observations cover only a tiny fraction of the Milky Way.Aims. In this paper, we study the prospects of expanding the CR measurements to very and ultra-high energies and remote parts ofthe Galaxy with the current and next-generation detectors.Methods. Based on calculations of fluxes expected from MCs, we formulate the requirements to the sensitivity of the post-Fermi-LAT detectors to map GeV-TeV CRs in the Galactic Disk. We also explore the potential of the current and future air-shower andatmospheric Cherenkov telescope arrays for the extension of CR studies to multi-TeV and PeV energy bands.Results. We demonstrate that the improvement of the Fermi-LAT sensitivity by a factor of a few would allow a dramatic increase inthe number of detectable MCs covering almost the entire Galaxy. The recently completed LHAASO should be able to take the firstCR probes at PeV energies in the coming five years or so.

Key words. cosmic rays, Gamma rays: ISM, ISM:clouds

1. Introduction

The paradigm of Galactic cosmic rays (CRs) assumes that the lo-cally measured CR density (ρ�(1GeV) ∼ 1 eV/cm3), representsthe average level of CRs in the Galactic Disk (GD) (see, e.g. Am-ato & Casanova (2021)). During their confinement in the GD,CRs mix and lose track of their production sites, creating theso-called "CR sea". The spatial distribution of CRs in the MilkyWay depends on the distributions of CR sources and the diffusioncoefficient characterizing the CR propagation in GD. It is be-lieved that the mixture of CRs caused by diffusion is so effectivethat one should expect uniform distribution of CRs throughoutthe Galaxy with almost constant level of the "CR sea". However,significant deviations of the density cannot be excluded both onsmall (tens of parsecs) scales because of the concentration of ac-tive or recent CR accelerators and on large (kiloparsec) scalesdue to the spatial variations of the CR diffusion coefficient.

The locally measured CR fluxes give direct informationabout the "CR sea level" only in a single point in the MilkyWay. Meanwhile the measurements of the "CR sea" levelthroughout the Galaxy is of paramount importance. Low-energy(MeV/GeV) CRs play a significant role in the regulation of theionization, chemistry, and the dynamics of the gas and dust, andconsequently on the star and planet formation (Padovani et al.2020). Moreover, CRs might have a non-negligible impact onthe habitability of planets around other stars (Atri et al. 2014).At very high energies, the influence of CRs on these processesis less pronounced. However, the information about the distribu-

tion of highest energy CRs in the GD is essential for searchingfor CR TeVatrons and PeVatrons in the Milky Way.

Gamma-ray astronomy provides a unique channel for inves-tigating the distribution of CRs far from the Solar System. Ofparticular interest is the gamma-ray emission produced at in-teractions of CRs with the interstellar medium (ISM) whichprovide straightforward information on the CR content at thelocation of the interaction. The observations with the Fermi-Large Area Telescope (LAT) demonstrated the feasibility of thismethod: CR densities have been extracted both from studiesof the diffuse gamma-ray emission emission (Acero et al. 2016;Yang et al. 2016; Pothast et al. 2018) and from giant molecularclouds (GMCs) (Yang et al. 2015; Neronov et al. 2017; Aharo-nian et al. 2020; Peron et al. 2021). The latter, being small re-gions of enhanced gas density, provide localized information onthe CR content with accuracy better than 100 pc.

Fermi-LAT is the only instrument that succeeded in exten-sively measuring the γ-ray flux from "passive", i.e. a cloud with-out having in the proximity of currently operating CR sources,GMCs. Yet, the detection is limited to exceptionally massive (&106 M� ) or nearby (d. 1 kpc) clouds, if the illuminating CRflux coincides with the local flux of cosmic rays, J�.The softpower-law spectrum of the "CR sea" (α� ∼ 2.7) makes the stud-ies at TeV and higher energies very difficult. The HAWC Col-laboration reported upper flux limits from local molecular clouds(Abeysekara et al. 2021) which agree with the above assessment.Meanwhile, the H.E.S.S. Collaboration reported the detection atTeV energies of a GMC located in the galactic plane that shows

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enhanced emission at GeV energies (Sinha et al. 2021). The ad-vent of new and improved γ-ray instruments opens up new pos-sibilities for the exploration of the sea of galactic cosmic raysin the near future. The Cherenkov Telescope Array (CTA) is de-signed to reach a sensitivity 10 times better than H.E.S.S. whichis promising for detection of at least a few "passive" molecu-lar clouds. Even more optimistic assessment can be applied toultra-high-energy (UHE) gamma-rays thanks to the dramatic im-provement of the flux sensitivity above 100 TeV by the LargeHigh Altitude Air Shower Observatory (LHAASO) (Cao 2021).

Below we discuss the perspectives of detection of gamma-rays from GMCs in high, very-high and ultra-high energy bands.

2. Cosmic Ray interaction in molecular clouds

The inelastic interaction of CRs with the interstellar gas result inproduction of secondary unstable products, first of all π-mesons,which decaying, produce gamma-rays, neutrinos and electrons.The gamma-ray emissivity induced in MCs by penetrating CRsdepends on (i) the energy distribution of CR protons J(Ep), (ii)the density of the ambient hydrogen, and (iii) the content ofheavier elements both in the projectile cosmic-rays and in am-bient gas, quantified by the parameter ξN . The resulting flux atEarth, is given by:

Fγ(Eγ) = ξNMd2

∫dEp

dσpp→γ(Ep, Eγ)dEγ

J(Ep) ∝ A ξN φγ(Eγ),

(1)

where A ≡ M5/d2kpc (M5 ≡ M/105 M�, dkpc = d/1 kpc) is re-

lated to the column density of the targeted material and dσ/dEγ

is the differential gamma-ray cross section of proton-proton in-teractions as calculated by Kafexhiu et al. (2014) for the broadinterval from the threshold of pion production ≈ 280 MeV toPeV energies.

The local spectrum of protons, J�, has been measured withgreat precision in the Earth’s vicinity (e.g. AMS (Aguilar et al.2015), DAMPE (Amenomori et al. 2021)), from Earth (e.g.KASCADE (Apel et al. 2013), Icetop (Aartsen et al. 2019)), andnow as well outside the Solar System (Stone et al. 2019), wherethe CR spectrum does not suffer solar modulation. Recent mea-surements revealed that the CR proton spectrum doesn’t havea single power law shape; the spectral index Γ changes from2.8 below ∼ 700 GeV to 2.6 up to 15 TeV and steepens again(Γ ≈ 2.85 at higher energies (Lipari & Vernetto 2020). Above1 PeV, CR measurements are provided by ground-based detec-tors. The interpretation of indirect measurements depends on theinteraction models, therefore they remain controversial. More-over, the lack of any measurements between 100 TeV and 1 PeVintroduces additional uncertainties both in the proton spectrumand composition of heavier nuclei. This issue is comprehensivelydiscussed by Lipari & Vernetto (2020). Fig.1 shows the recentlocal measurements of the CR proton fluxes. The black line hasbeen obtained using the fitting parameters derived by Lipari &Vernetto (2020) above 100 GeV, while below 100 GeV, to ac-count for the solar modulation, the curve matches the data ofVoyager to the data of AMS as done in Vos & Potgieter (2015)

At low energies, for the standard compositions of the in-terstellar medium and CRs, the contribution of nuclei to thegamma-ray production is comparable to the contribution fromthe pp-interactions, namely ξN ≈ 1.8 (Mori 2009). At higher en-ergies, especially around the knee at PeV energies, CRs become

10−2 100 102 104 106 108

Energy [GeV]

10−6

10−5

10−4

10−3

10−2

10−1

100

E2 x F

lux

[GeV

cm

−2 s

−1]

Voyager [Cumm ngs et al. 2016]AMS02 [Agu lar et al. 2015]DAMPE [An et al. 2019]KASCADE [Apel et al. 2013]ICETOP [IceCube coll. 2019]

Fig. 1. The local spectrum of cosmic ray protons as measured by differ-ent experiments (see the figure legend). The black line is the interpola-tion of the experimental points using the fitting parameters reported byVos & Potgieter (2015) and Lipari & Vernetto (2020) below and above100 GeV, respectively The dotted part represents protons below the en-ergy threshold of 280 MeV, which do not participate in the π-mesonproduction.

"heavier"; consequently the nuclear enhancement factor ξN in-creases with energy. The significant uncertainty in the CR com-position in the knee region introduces non-negligible uncertaintyin ξN . The calculations based on the available CR data show thatξN progressively increases from 1.8 at 10 GeV to ' 2.6 at 1 PeV.

The third parameter that determines the cloud’s flux is A =M5/d2

kpc which is the measure of the column density of the gasembedded in the cloud. Indeed, given that M = Ncolθd2, we haveA ∝ Ncolθ where θ is the angular area of the considered region.It can be presented in the form:

A = 8 × 10−20∑l,b

(Ncol(l, b)cm−2

)dldb

180

)2(2)

where dl and db are the pixel size of the gas tracer map. Remark-ably, A is independent of uncertainties both in the mass of thecloud and the distance. The only relevant uncertainty is related tothe column density and comes from the tracers of molecular gas.The most commonly employed tracers are the 12CO(J=1→0)line that brings an uncertainty of the order of 30% (Bolatto et al.2013) in the gas density and the dust opacity with an uncertaintythat amounts to ∼ 20% (Ade et al. 2011).

3. Molecular Clouds in the Milky Way

From the recent analysis of the all-Galaxy CO survey of Dame,Hartmann and Thaddeus (Dame et al. 2000), Miville-Deschêneset al. (2016) identified more than 8000 MCs distributed allthroughout the galactic plane. When inspecting the clouds ofMiville-Deschênes et al. (2016), hereafter MD16, we see thatmost of the clouds have a low A parameter (see Fig 2), below0.4, which was determined in Aharonian et al. (2020) to be a safethreshold for spectral measurements of clouds of different ex-tensions, located both in the inner and outer parts of the Galaxy.These considerations were based on the assumption that the levelof CRs that illuminates the cloud is coincident with the locallevel of CR, J�, which was taken as a reference value. Among theM16 catalog clouds, less than 1% is above the detection thresh-old of Fermi-LAT; the fraction is even lower when considering

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G. Peron and F. Aharonian: Probing the galactic cosmic-ray density with current and future γ-ray instruments

0 0.2 0.4 0.6 0.8 1 1.5 2 2.5 3100

101

102

103

104 96.21%

3.47%

0.21%

0.02%

0.0%

0.01%

57.89%

2.91%

0.19%

Inner Galaxy ( l <60 ∘

All Galaxy

0.0 0.1 0.2 0.3 0.4A

101

102

103

37.5%

12.2%5.4%

2.8%1.8%

0.6%0.4%

0.2%

Inner Galaxy ( l <60 ∘

Whole Galaxy

0 0.2 0.4 0.6 0.8 1 1.5 2 2.5 3A

100

101

102

103

104 96.21%

3.47%

0.21%

0.02%

0.0%

0.01%

38.32%

0.56%

0.02%

Outer Galaxy ( l ∘60 ∘

All Galaxy

0.0 0.1 0.2 0.3 0.4A

100

101

102

103

31.39%

4.67%1.55%

0.7%0.27%

0.12%0.15%

0.01%

Outer Galaxy ( l ∘60 ∘

Whole Galaxy

Fig. 2. Histogram of the A parameter of molecular clouds from theMD16-catalog. The black-contoured bars include all the clouds in thecatalog, while the grey bars correspond, in the upper panel, to MCs inthe inner Galaxy (|l| < 60◦), and to MCs in the outer Galaxy (|l| > 60◦),in the lower panel. The number fraction with respect to the total is alsoreported as percentages. The inset panels zoom the parameter range be-low 0.4 determined as the detection threshold of MCs by Fermi-LAT(Aharonian et al. 2020).

only the inner (|l| < 60◦) Galactic regions (∼0.3%). For the outerGalaxy, the threshold can be lowered by a factor of 2. Howeverthis part of the Galaxy hosts less dense clouds, with A parametersin most cases lower than 0.6 and which overcomes the detectionthreshold only for the ∼ 1% of the cases, even when loweringthe threshold to A =0.2. This means that most of the "CR Sea"cannot be explored by Fermi-LAT. In particular, ∼15% of themolecular clouds, corresponding to more than 1000 MCs, havean A factor between 0.1 and 0.4, just below the Fermi-LAT de-tection threshold.

In addition to emissivity, source confusion affects the de-tectability of clouds in γ-rays. Confusion can arise both due tothe proximity of known γ-ray sources, and due to other cloudslocated on the same line of sight.

3.1. Overlaps with other gamma ray sources

We included into consideration all reported GeV and TeV γ-raysources from the 4FGL (Fermi-LAT; The Fermi-LAT collabora-tion (2019)), HGPS (HESS Galactic Plane Survey, Abdalla et al.(2018)) and the 3HWC (HAWC; Albert et al. (2020) ) catalogswhich lie within the radius of 1.1 θ, where θ is the angular sizeof the cloud:

– 75 % of clouds do not have an overlapping source– 3 % of clouds have at least one overlapping known source– 22 % of clouds have only unidentified overlapping sources– 63% of the clouds do not have nearby sources within 0.5◦.

Clouds without nearby sources are ideal to test the "CR Sea",even though this does not exclude possible contributions of yetunresolved gamma-ray sources.

3.2. Fraction of gas on the line of sight

Differently from the smoothly distributed atomic gas, the molec-ular component of the interstellar medium (ISM) is clumpy andmostly concentrated in dense clouds. Miville-Deschênes et al.(2016) pointed out that the line of sight column densities in most(≈60%) directions are contributed by three or fewer molecularclouds; in the 20% of cases, the column density is dominated bya single cloud. Following the approach proposed by Peron et al.(2021), one can derive a relation between the maximum fractionof back- and fore-ground gas (X) which can be on the line ofsight of a cloud and the level of excess (N) with respect to thelocal γ-ray emissivity (φγ(J�)), which can be detected:

X <0.7N

0.7N + 1.3(3)

For example, if a cloud has an emissivity larger than the nom-inal value, by a factor of N = 4, it would be detected if the frac-tion of background gas is X < 0.68 or, in other words, if the frac-tion of column density belonging to the cloud is at least 32%. Fordetection of the local CR Sea in molecular clouds (N = 1), thefraction of gas in the cloud has to be at least 65%. This guaran-tees the distinction of the cloud above the background gas, evenwithout subtracting the contribution of the latter. Otherwise, theflux of the cloud, even if enhanced, would be masked by theγ-ray flux of the back- and foreground gas. To avoid this, it isnecessary to model the back- and fore-ground gas as a separatesource, as done for example in Aharonian et al. (2020). This ap-proach, however, is subject to large uncertainties of the CO andHI measurements, which are the only tracers that can be used for3-dimensional decomposition. Notice nevertheless that, evenwithout a 3-dimensional decomposition, measuring a flux sim-ilar to J� coming from a column of gas, is a strong indicationthat the entire column is emitting at a similar level as the localCR sea. The local flux can be considered a minimum level, asno lower flux has been recorded so far, except for the outermostpart of the Galaxy, which are far from the highest concentra-tion of Supernova Remnants (SNRs) and Pulsar Wind Nebulae(PWNe).

We calculated the fraction of gas belonging to each cloud ofthe MD16 catalog relative to the total gas in the l.o.s. includedin the area of the cloud from the brightness of the CO, WCO:

ρ =

∫ l+θl−θ dl

∫ b+θ

b−θ/2 db∫ v+2√

2 log 2σv

v−2√

2 log 2σv

dv WCO(l, b, c)∫ l+θl−θ/2 dl

∫ b+θ

b−θ db∫ +∞

−∞dv WCO(l, b, c)

, (4)

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0.0 0.2 0.4 0.6 0.8 1.0100

101

102

0-2 kpc

0.1<A<0.4A>0.4

0.0 0.2 0.4 0.6 0.8 1.0100

101

102

2-4 kpc

0.0 0.2 0.4 0.6 0.8 1.0100

101

102

4-6 kpc

0.0 0.2 0.4 0.6 0.8 1.0100

101

102

6-8 kpc

0.0 0.2 0.4 0.6 0.8 1.0

101

102

8-10 kpc

0.0 0.2 0.4 0.6 0.8 1.0100

101

102

10-20 kpc

ncol, cloud/ncol, tot

Fig. 3. Distribution of the ratio of the cloud’s column density to thetotal column density in the direction of the cloud for different intervalsof distances from the Galactic Center. Only the clouds not overlappingwith Fermi-LAT γ-ray sources are shown. The clouds characterized bythe parameter A > 0.4 (solid grey) and 0.1 < A < 0.4 (hatched) arehighlighted.

where θ is the angular size of the cloud, v is the radial velocity,and σv is the dispersion of the velocity profile assumed to beGaussian. The results are shown in 3 for clouds not overlapping(within 1.1 θ) with any cataloged Fermi-LAT source. It appearsthat only a handful of clouds satisfy the condition of detectabil-ity. The limiting factor is given by the threshold of A > 0.4 im-posed by the sensitivity of Fermi-LAT. More than 50 clouds with0.2 < A < 0.4 are the dominant objects on the line of sight, hav-ing ρ > 0.65. This number rises to 200 if we lower the thresholdto A = 0.1.

4. The potential of current gamma-ray instruments

Fermi-LAT is a powerful large field-of-view gamma-ray detec-tor with the best performance at GeV energies. It is well de-signed to explore extended galactic sources, particularly SNRsand PWNe. This also concerns GMCs; however, the sensitivityof Fermi-LAT is at the margin of detection of gamma-rays fromonly a handful GMCs unless the CR density in the vicinity ofthe clouds does not substantially exceed the local level. Anotherproblem is the energy coverage. Because of the steep spectrum

and the limited detection area of Fermi-LAT, the detection ofgamma-rays even from the most favorable "passive" GMCs withA ∼ 1 cannot be extended beyond 0.1 TeV. The range of TeVenergies is the domain of ground-based detectors - Imaging At-mospheric Cherenkov Telescopes (IACTs) and air shower parti-cle arrays. However, for the current detectors, particularly HESSand HAWC, GMCs illuminated by J� are not accessible.

This can be seen in Fig. 4 where the flux sensitivities ofthe currently operating detectors are shown together with theflux induced by the local CR Sea on a cloud with A = 1,calculated with Eq.(1). In the plot are displayed: the sensitiv-ity achieved after 10 years observations with Fermi-LAT for theinner (l, b = (0, 0); dark red) and outer (l, b = (0, 30); light red)Galaxy (Maldera et al. 2019); the H.E.S.S. sensitivity for 100hours observation with the 4-telescopes configuration (solid yel-low) (Funk & Hinton 2013) and the preliminary calculation ofthe sensitivity for the 5-telescopes configuration (yellow dashed;Holler et al. (2015)); the HAWC sensitivity for 5 years of ob-servations (green;HAWC (2020)); and the LHAASO sensitivityfor 1-year observations (magenta; Di Sciascio (2016)). The γ-rayflux of the given cloud exceeds the sensitivity of current instru-ments only at GeV energies.

The condition for visibility of a molecular cloud can be deter-mined by imposing that the flux of a cloud is higher or equal thanthe sensitivity, S (t, E), calculated for a certain exposure time, t:

F(E) ≥ S (t, E) (5)

Aφγ(E) ≥

√t0t

S 0(E) (6)

A√

tt0≥

S 0(E)φγ(E)

≡ R0(E) (7)

here S 0 is the sensitivity calculated at a specific exposure t0. Inthis sense R0 represents a condition for visibility as it is the mini-mum ratio to detect a cloud of A = 1, which is characterized by aemissivity φγ with an instrument of sensitivity S 0(E) calculatedfor a t0-long exposure.

The values for R0 for the current γ-ray instruments are plot-ted (dotted curves) in Fig 6, for the assumption of the localgamma-ray emissivity φγ = φγ(J�). One can see that in orderto measure a similar emissivity as the local one with the cur-rent TeV instruments, at least a R0 of ∼ 3 should be obtained.No single cloud in the Galaxy is characterized by A ∼ 3, ex-cept for some of the Gould Belt’s clouds. However, these nearbyclouds are very extended, thus the sensitivity is significantly re-duced. The sensitivity for a source of extension θ compared tothe point-like source is worsened by the factor:

ω(E, θ) =

√θ2 + σ2

PS F(E)

σPS F(E), (8)

where σPS F is the instrument’s point spread function. This re-sults in a stricter condition on the visibility factor:

R(E, θ) = ω(θ, E)R0 = ω(θ, E)S 0(E)F0(E)

(9)

The worsening is especially significant for imaging airCherenkov telescopes (IACTs) having the best angular resolu-tion of 0.05-0.1◦ or better (see the top panel of Fig 7). The ef-fect is less dramatic for water Cherenkov (WC) detectors, whichhave a point spread function (PSF) of 0.1-0.3◦, comparable to

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G. Peron and F. Aharonian: Probing the galactic cosmic-ray density with current and future γ-ray instruments

the Fermi-LAT one and to the typical angular extensions of mostof the clouds in the Galactic plane.

The exposure time is another important factor for the de-tectability of GMCs. IACTs are pointed telescopes with a small(a few degrees) FoV, while WC detectors cover simultaneouslya significant fraction of the sky. The typical exposure time forspecific segments of the Galactic Plane during the survey of thelatter by IACTs over several years could be as large as 100 hours,which however is not sufficient to detect TeV gamma-rays from"passive" GMCs if illuminated by the local CR flux.

The exposure time of a large fraction of clouds in the Galaxyby large FoV ground-based air shower particle detectors is muchlarger; it can be as large as 2000 hours per year (approximately6 hours per night). Nevertheless, to observe passive clouds withHAWC, at least a factor R = 10 is needed, which is too large tobe reached only with the exposure time increase.

The recently completed Water Cherenkov Detector Array(WCDA) of LHAASO will be able to detect a limited numberof passive GMCs between 1 and 10 TeV. A breakthrough is ex-pected at higher energies, thanks to the superior sensitivity ofthe KM2A (square km array) of LHAASO. For KM2A, R . 1after five years of observations, making the ultrahigh energies aseffective as Fermi-LAT at GeV energies, for searches of gamma-ray emitting clouds (see Fig.5).

4.1. Analysis technique

The recent advent of the gammapy software package Deil et al.(2017) allows us to apply the 3D-likelihood technique, initiallyused in the analysis of GeV data, also to the study of very-high-energy data. This is an essential tool for faint and extendedgamma-ray sources. Compared to the traditional methods (Bergeet al. 2007) based on the subtraction of the background calcu-lated in an ‘off’ region, the 3D likelihood analysis has certainadvantages. It allows separation of the background caused bythe hadronic showers from the large scale diffuse emission and,therefore, is more sensitive to low-surface-brightness sourceswith fluxes comparable to the diffuse gamma-ray emission ofthe galactic disk. Besides, the simultaneous fitting of all sourcesin the region of interest and the possibility of defining a spatialtemplate based on observations on other wavelengths helps toresolve the cases of crowded areas. Note that the exploitation ofthese factors leaded to the first successful detection of a passiveGMC at TeV energies (Sinha et al. 2021).

4.2. Runaway cosmic rays

The detectability of a cloud in γ-rays is significantly improvedin the case of location of the cloud in the environment withenhanced CR density caused by the presence in the proximityof recent and currently operating accelerator(s). Runaway CRs,i.e. particles which already have left the accelerator and injectedinto the circumstellar medium have been registered both at GeVand TeV energies in the vicinity of some middle-aged super-nova remnants, (e.g. W44 (Peron et al. 2020), W28 (Aharonianet al. 2008)). The spectrum of runaway particles close/inside theclouds is hard to predict as it depends on different conditionssuch as the age of the accelerator, the distance of the clouds andof the diffusion coefficient Aharonian & Atoyan (1996). Mean-while, the flux can be enhanced, e.g. in the surroundings of W44(Peron et al. 2020), by order of magnitude compared to the localCR flux. If the injection occurs in a continuous regime, as in thecase of massive star clusters, the CR density is expected to be

strongly peaked towards the the accelerator, therefore could beenhanced around the latter by orders of magnitude (Aharonianet al. 2019). Observations of the escaped particles are funda-mental to understand the entire acceleration power of a source(Gabici et al. 2007) and new and future γ-ray instruments willhelp in constraining the spectrum of escaped particles at thehighest energies.

5. The prospects

The next generation of instruments will include the Cherenkovtelescope array (CTA) and the Southern wide-field gamma-rayobservatory (SWGO). The first will reach a sensitivity 10 timesbetter than H.E.S.S., with an angular resolution close to 3 ar-cmins. Such an improved sensitivity would be promising to de-tect passive molecular clouds because in the case of CTA R ∼0.5 at 1 TeV. The improved sensitivity, together with the betterangular resolution, make CTA an ideal instrument to study notonly the spectral energy distribution but also to investigate thespatial distribution of CRs inside the cloud itself. SWGO as wellwill reach a sensitivity an order of magnitude better than HAWCtherefore it could be a valid counterpart of WCDA-LHAASO inthe southern hemisphere, where the most massive clouds are lo-cated. Nevertheless, even with the improved sensitivity of theforthcoming gamma-ray telescopes, the measurements will re-main limited to a handful of clouds in the VHE regime.

Meanwhile, even a relatively moderate (by a factor of 2-3) improvement of the Fermi-LAT sensitivity at GeV energieswould dramatically increase the number of clouds and thus pro-vide a probe of the CR pressure (energy density) throughout thesubstantial fraction of the Galactic Disk. Achieving such an im-provement in sensitivity is not a trivial task. Given that GeV γ-rays are detected in the background-dominated regime, the min-imum detectable flux (sensitivity) decreases with the exposuretime as t−1/2. Therefore, the resource of 12-year old Fermi-LATin this regard is rather limited. Even assuming that Fermi-LATwill continue observations for another decade, the gain in thesensitivity cannot exceed 40 %. Clearly, one needs a new, moresensitive detector of GeV γ-rays. The improvement of sensitivityfor the specific task of detection of γ-rays from extended GMCscannot be realized by improving the angular resolution. Tak-ing Fermi-LAT 10-yr sensitivity as reference, Fig. 7 shows howenlarging the exposure time by a factor τ or the size of the detec-tor by a factor Λ affects the sensitivity. A breakthrough can beachieved only through an order of magnitude (Σ > 3) increaseof the detection area. Thus, we will need a new Very large areatelescope (VLAT) to achieve our goals. This is a challengingbut still feasible task for the space-based instruments; see, e.g.the recent proposal for the Advanced Particle-astrophysics Tele-scope (APT) (Buckley et al. 2019). An improvement of the sen-sitivity of a factor Σ ∼3 can already be achieved by observingfor 15 years with a Fermi-like instrument of size (3×3) m2. TheAPT aims at having a ∼10 times larger effective area comparedto the Fermi-LAT. Two designs have been proposed: a (3×3) m2

instrument and a (3×6) m2 one. It is clear that, if this project willbe approved, it will be an ideal instrument for our scopes.

5.1. Probing the CR sea

With its current sensitivity, the Fermi-LAT can map at most 1%of the molecular clouds identified in the MD16-catalog. Thiscorresponds to 40 objects, of which only 10 belong to the in-ner Galaxy. Lowering the sensitivity of a factor Σ = 3 wouldincrease the detectable sources to more than 1300 in total, of

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Fig. 4. Gamma-ray fluxes expected from a GMC with A=1 compared to the point-like source sensitivities of currently operating γ-ray instruments:the 10-year Fermi-LAT sensitivity for the outer (light red) and inner Galaxy (dark red); the H.E.S.S. 5-telescope system sensitivity for 100 hr (solidyellow); the HAWC 5-years sensitivity (green); and the LHAASO 1-year sensitivity (solid violet). The black solid line is the flux of a molecularcloud of A = 1 illuminated by the "CR Sea". The two spectra above 104 GeV represents two options of CR proton spectra based on the spectrareported above 106 GeV by the KASCADE (dashed line), and ICEtop (dotted line) collaborations (see the text). As a reference, the fluxesrepresenting 10, 1 and 0.1 percent of the gamma-ray flux from the Crab Nebula (Cao et al. 2021) are shown.

which ∼200 in the inner Galaxy (< 4 kpc). The spatial distribu-tion of the detectable MCs from the MD16-catalog is plotted inFig. 8. With a factor Σ = 3 improvement, all galactic rings willbe sampled with sufficient clouds, especially the 2–4 kpc ring,which is the most difficult to analyze because it is projected ina small range of longitudes, and therefore several sources mayoverlap.

Finally, while Fermi-LAT is limited to the observation ofmolecular clouds relatively close to the galactic plane, an ad-vanced detector with improved sensitivity would allow accessto several locations up to 400 parsecs above the plane (see thelower panel of Fig. 8). The combined knowledge of the cosmic-ray density at different distances from the Galactic Centre andat different heights from the Galactic plane would improve theknowledge regarding the propagation properties of these high-energy particles in the radial and perpendicular directions.

6. Conclusions

Gamma-ray emitting GMCs play a unique role of CR barom-eters allowing deep probes of the pressure (energy density) ofCRs throughout the Galactic Disk with far-going astrophysicalimplications.

The γ-ray fluxes from GMCs are faint and extended, whichmakes their detection difficult. Yet, the analysis of Fermi-LATobservations of the Galactic Disk revealed γ-rays from a lim-ited number of GMC in the energy interval between 1-100 GeV(Aharonian et al. 2020; Peron et al. 2021; Baghmanyan et al.2020). These results convincingly demonstrate the power of the

method. At the same time, they indicate that the potential ofFermi-LAT concerning the studies of GMCs is almost saturated.For deeply probing CRs in different, including remote parts ofthe Galactic Disk, we need a new advanced γ-ray detector inthe GeV band (a "V-LAT") with sensitivity improved, comparedto Fermi-LAT, by a factor of few. Hopefully, such a detector willappear in the foreseeable future. Such an instrument will be ben-eficial not only for effectively probing the CR "Sea" but also forsearching of dark matter, investigating the nature of gamma-raybursts and resolving other faint sources.

Although with the increase of energy, the detection of GMCsin γ-rays becomes more challenging, the CTA, as well as the wa-ter Cherenkov detectors like the proposed SWGO and currentlyoperating WCDA-LHAASO, should be able to detect γ-rays inthe energy interval between 1 to 10 TeV from GMCs charac-terised by the parameter A & 0.5. The domain of ultra-high en-ergy γ-rays from 30 TeV up to 1 PeV looks even more promis-ing. One may predict that the recently completed and presentlyworking in its full power KM2A-LHAASO in the coming yearswill detect GMCs in ultra-high energies and thus contribute sig-nificantly to uncovering the origin of highest energy CRs aroundthe knee and beyond.

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10−2 10−1 100 101 102 103 104 105 106Energy [GeV]

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Fig. 6. R values calculated for the current instruments (upper panel):Fermi-LAT (red), H.E.S.S. (yellow),HAWC (green), LHAASO (1-year;violet) and next-generation instruments (lower panel): VLAT (blue),CTA (orange), SWGO (cyan), LHAASO (5-years; violet). The expo-sure times are the same as in Figs 4 and 5. The curves refer to the pointsource hypothesis (dotted lines) and to a 0.5◦-wide source (solid lines).

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Fig. 8. Spatial distribution of the clouds from the MD16-catalog in the (Xgal,Ygal) plane (upper panel) and in the (Rgal, Zgal) plane (lower panel).In the left, the molecular clouds that overcome the detection threshold of Fermi-LAT and of an advanced detector with improved sensitivity Σ = 3are indicated in dark-red, and blue, respectively. In the right, the clouds visible by LHAASO after 5 (light purple) and 10 (dark purple) years ofobservations are indicated. In the latter we assumed the same performance in the entire Galaxy, even though the sensitivity in the inner Galaxyshould be worse. The size of the clouds is considered and an average angular resolution of 0.5◦ and 0.3◦ are assumed for Fermi-LAT and LHAASO,respectively.

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