Prospects of Newly Detecting Nearby Star-Forming Galaxies by the Cherenkov Telescope Array

MNRAS 000, 1–9 (2020) Preprint 3 November 2020 Compiled using MNRAS LATEX style ﬁle v3.0

Prospects of newly detecting nearby star-forming galaxies by the Cherenkov Telescope Array

Naoya Shimono,1★ Tomonori Totani,1,2 Takahiro Sudoh1 1Department of Astronomy, the University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan 2Research Center for the Early Universe, the University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan

Accepted XXX. Received YYY; in original form ZZZ

ABSTRACT Prospects of the Cherenkov Telescope Array (CTA) for the study of very high energy gamma- ray emission from nearby star-forming galaxies are investigated. In the previous work, we constructed a model to calculate luminosity and energy spectrum of pion-decay gamma-ray emission produced by cosmic-ray interaction with the interstellar medium (ISM), from four physical quantities of galaxies [star formation rate (SFR), gas mass, stellar mass, and effective radius]. The model is in good agreement with the observed GeV–TeV emission of several nearby galaxies. Applying this model to nearby galaxies that are not yet detected in gamma rays (mainly from the KINGFISH catalog), their gamma-ray luminosities and spectra are predicted. We identify galaxies of the highest chance of detection by CTA, including NGC 5236, M33, NGC 6946, and IC 342. Concerning gamma-ray spectra, NGC 1482 is particularly interesting because our model predicts that this galaxy is close to the calorimetric limit and its gamma-ray spectral index in GeV–TeV is close to that of cosmic-ray protons injected into ISM. Therefore this galaxy may be detectable by CTA even though its GeV flux is below the Fermi sensitivity limit. In the TeV regime, most galaxies are not in the calorimetric limit, and the predicted TeV flux is lower than that assuming a simple relation between the TeV luminosity and SFR of M82 and NGC 253, typically by a factor of 10. This means that a more sophisticated model beyond the calorimetric limit assumption is necessary to study TeV emission from star-forming galaxies. Key words: gamma-rays: galaxies – galaxies: starburst

1 INTRODUCTION (Acero et al. 2009; VERITAS Collaboration et al. 2009; H. E. S. S. Collaboration et al. 2018), and more detections in TeV are expected All galaxies with substantial star formation activity (star-forming by the Cherenkov Telescope Array (CTA) project. A large sample galaxies, SFGs) are gamma-ray emitters. Gamma rays are produced of gamma-ray emitting SFGs in GeV–TeV in the near future will be by the decay of pions, which are produced by collisions of cosmic- useful to study the production and propagation of cosmic rays in ray protons accelerated by supernova remnants with the interstellar various types of galaxies. It is then important to prepare theoretical medium (ISM). This process is dominant in the diffuse Galactic predictions for gamma-ray luminosities and spectra of nearby SFGs. gamma-ray background radiation (Abdo et al. 2009). Observing this gamma-ray emission from extragalactic galaxies is not easy because The most popular approach to predict gamma-ray luminosity of smaller luminosities compared with those of active galactic nuclei from a galaxy is to relate it with some of physical quantities of (AGNs) such as blazars, but in recent years an increasing number the galaxy, especially the star formation rate (SFR). Gas mass of a of nearby SFGs [the Large and Small Magellanic Clouds (LMC and galaxy is often additionally used to take into account the interac- SMC), M31, NGC 253, M82, NGC 4945, NGC 1068, NGC 2146, tion of cosmic rays with ISM (Torres 2004; Domingo-Santamaría Arp 220, Arp 299, and M33] have been detected in the GeV band & Torres 2005; Persic et al. 2008; Lacki et al. 2010; Inoue 2011; by the Fermi satellite (Abdo et al. 2010a,b,c,d; Ackermann et al. Lacki et al. 2011; Wang & Fields 2018). In other modelings, micro- 2012b; Tang et al. 2014; Peng et al. 2016; Lopez et al. 2018; Ajello physical parameters about cosmic-ray propagation (e.g. magnetic et al. 2020; Xi et al. 2020a,b), proving that gamma-ray emission field strengths, convection velocities, or mean free paths) are intro- from SFGs is indeed ubiquitous. M82 and NGC 253 were detected duced as free parameters and these are fit to reproduce the observed also in the TeV band by ground-based air Cherenkov telescopes gamma-ray luminosity of a galaxy (Yoast-Hull et al. 2013, 2014; Eichmann & Becker Tjus 2016; Peretti et al. 2019; Krumholz et al. 2020). In a more detailed approach, cosmic-ray production and ★ E-mail: [email protected] propagation are numerically simulated within a galaxy, though it is

© 2020 The Authors 2 Shimono et al. difficult to adopt such an approach to predict gamma-ray emission are modified from those in S18. For the consistency with the KING- from a variety of nearby galaxies (Martin 2014; Pfrommer et al. FISH catalog (see §3), SFR, gas mass, and stellar mass except for 2017; Chan et al. 2019). those of MW are derived in the same way as Rémy-Ruyer et al. In the previous work, we constructed a model to predict (2014, 2015). SFRs are derived from H훼 and IR luminosities using gamma-ray luminosity and spectrum of a SFG, from four input eq. (11) in Kennicutt et al. (2009), and IR luminosities are esti- parameters (SFR, gas mass, stellar mass, and effective radius) that mated from eq. (5) in Dale & Helou (2002) using the IRAS data are easily available for nearby galaxies [Sudoh et al. (2018), here- (Sanders et al. 2003). Gas mass is the sum of neutral and molecular after S18]. The escape time scale of cosmic-ray protons is estimated hydrogen masses. Neutral hydrogen mass is derived from 21-cm as a function of the proton energy, considering diffusion in turbu- line flux, and H2 mass is derived from CO(1-0) line flux assuming 푋 ∝ 푍−2 lent magnetic fields and advection. It was found that this model a metallicity-dependent conversion factor ( CO−H2 ). Stellar reproduces the observed gamma-ray luminosities of nearby galax- mass is estimated using the equation derived in Eskew et al. (2012) ies better than those using only SFR and/or gas mass of galaxies. In using the Spitzer data (Dale et al. 2009). this paper, we apply the S18 model to nearby galaxies that are not Figure 1 shows the comparison of our model and the observed yet detected in the TeV band (mainly from the KINGFISH catalog), gamma-ray luminosities by Fermi, showing that our model is in good predict their gamma-ray emission properties, and discuss their re- agreement with observations, and performs better than the simpler lation to galactic physical parameters. Then the prospect of future assumptions such as 퐿훾(0.1–100 GeV) ∝ 휓 (the calorimetric limit) studies with CTA will be discussed. or 퐿훾(0.1–100 GeV) ∝ 휓푀gas (intended to be the escape limit, In Section 2 our model is described, especially about some though 푀gas should be ISM density in reality). The data point for minor changes from the original S18 model. The nearby galaxy M33, which was not used to determine 퐶, is also shown here, and sample studied here will be presented in Section 3. Then results are the luminosity predicted by our model is in reasonable agreement presented in Section 4, followed by conclusions in Section 5. with the newly reported observed luminosity. Because NGC 253 and M82 have been detected in the TeV band, we show our model spectra 퐸훾 푑퐹훾/푑퐸훾, where 푑퐹훾/푑퐸훾 2 MODEL is differential energy flux per unit photon energy, in comparison with the observed data of these galaxies in Figure 2 to verify that We use the model constructed by S18. In this model, the proton our model works not only for GeV luminosity but also for GeV–TeV injection spectrum is formulated as: spectrum. Our model is in good agreement with the observed spectra − when we choose Γinj = 2.1–2.2. It should be noted that our model 푑푁 휓 퐸 푝 Γinj = 퐶 (1) spectrum for MW agrees with the observed spectrum of the diffuse 푑푡푑퐸 −1 푝 M⊙ yr GeV Galactic gamma-ray background (Ackermann et al. 2012a) when where 퐶 is determined by fitting the model to observed GeV lu- we set Γinj = 2.3 (S18). This means that our model can be applied minosities. Assuming a disk geometry for a galaxy, advection and to a wide range of SFGs with a single spectral index Γinj ∼ 2.2 for diffusion of cosmic rays are calculated for given proton energy by a the proton injection into ISM. one-zone modeling. The advection time is estimated by gravitational equilibrium along the perpendicular direction to the disc surface, and the magnetic field strength is estimated by equipartition with the 3 SAMPLE energy density provided by star formation activity. Then gamma-ray luminosity and spectrum are obtained by calculating the pion pro- The galaxy sample for this work is mainly constructed from the duction rate using ISM gas density, which is estimated from the gas KINGFISH catalog (Kennicutt et al. 2011), which includes a variety mass and galaxy size. This model does not consider the absorption of galaxy types for which SFR, gas mass, and stellar mass are of gamma rays by pair-production and the following cascade into compiled by Rémy-Ruyer et al. (2014, 2015). However, we removed lower energy photons. Pair-production optical depth is expected to NGC 1377 and 1404 from the sample, because SFR and/or gas mass become unity around 5 TeV for NGC 253 and M82 (Inoue 2011), are not available. The total number of KINGFISH galaxies used in and photons beyond this energy may be suppressed compared with this study is 59 (including NGC 2146, which is detected in the GeV our model predictions. See S18 for more detail of the model. band and listed in Table 1). The overall normalization parameter 퐶 is determined by fitting KINGFISH is not a complete sample about an observed flux, to the observed gamma-ray luminosities of nearby galaxies, which and some nearby galaxies that are promising for detection by CTA are the same as S18 and listed in Table 1. This is the only free may be missed. Therefore we made a simple estimate of TeV gamma- parameter that is fit to the observed gamma-ray properties in our ray flux for galaxies in the IRAS Revised Bright Galaxy Sample model. Note that galaxies whose AGN might contribute to gamma- (Sanders et al. 2003) and an H훼 imaging survey (Kennicutt et al. ray emission are removed (Ackermann et al. 2012b; Yoast-Hull 2008), assuming that TeV flux is proportional to SFR (i.e., the et al. 2017; Xi et al. 2020b), and that M31 is also removed because calorimetric limit). For clarity, we define the value 퐿훾 (푥) as its gamma-ray emitting region is different from gas distribution, 푑퐿훾 implying that the interaction between cosmic rays and ISM is not 퐿 (푥) 퐸 , 훾 = 훾 푑퐸 (2) the main source of gamma rays from this galaxy (Ackermann et al. 훾 푥 2017). After S18, gamma-ray detection has been reported for M33 where 푑퐿훾/푑퐸훾 is differential luminosity per unit photon energy. (Ajello et al. 2020; Xi et al. 2020a,b), along with a few more galaxies whose gamma rays might originate from AGN activities. We do not include this galaxy in the fitting, but gamma-ray luminosity 1 https://www.cta-observatory.org/science/ predicted by our model will be compared with these observations cta-performance/ later. 2 http://www.slac.stanford.edu/exp/glast/groups/canda/ In this paper, some physical parameters of galaxies in Table 1 lat_Performance.htm

MNRAS 000, 1–9 (2020) Prospects of newly detecting SFGs 3

Table 1. Physical properties of GeV-detected galaxies used to determine parameter 퐶.

푎 푏 푐 푑 푒 푓 Objects 퐷 퐿훾(0.1–100 GeV) 휓 푀gas 푀star 푅eﬀ − − (Mpc) (1039 erg s 1)(M⊙ yr 1)(109 M⊙)(109 M⊙) kpc

MW 0.82 ± 0.27 2.6 4.9 50 6.0 LMC 0.05 0.047 ± 0.005 0.3 0.59 1.8 2.2 SMC 0.06 0.011 ± 0.003 0.043 0.46 0.3 0.7 NGC253 3.5 12 ± 4 3.3 3.2 54.4 0.5 M82 3.3 14 ± 3 4.4 4.7 21.9 0.9 NGC2146 17.2 51 ± 27 11.4 10.4 87.1 3.0

푎 Distances taken from Kennicutt et al. (2008) for LMC, SMC and NGC 2146, Rekola et al. (2005) for NGC 253, and Foley et al. (2014) for M82. 푏 Gamma-ray luminosities taken from Ackermann et al. (2012b) except for NGC2146 from Tang et al. (2014). Note that the energy range is 0.2-100 GeV for NGC 2146 but 0.1-100 GeV for all other galaxies. 푐 Star formation rates calculated from Diehl et al. (2006); Makiya et al. (2011) for MW, and Sanders et al. (2003); Kennicutt et al. (2008, 2009) for all other galaxies. See also text. 푑 Total gas masses (atomic plus molecular hydrogens) calculated from Paladini et al. (2007); Rémy-Ruyer et al. (2014) for MW, Staveley-Smith et al. (2003); Israel (1997); Marble et al. (2010) for LMC, Stanimirovic et al. (1999); Israel (1997); Marble et al. (2010) for SMC, Springob et al. (2005); Knudsen et al. (2007); Pilyugin et al. (2014) for NGC 253, Chynoweth et al. (2008); Weiß et al. (2005); Moustakas et al. (2010) for M82, and Rémy-Ruyer et al. (2014); Young et al. (1989) for NGC 2146. 푒 Stellar masses taken from Bland-Hawthorn & Gerhard (2016) for MW, and Dale et al. (2009); Eskew et al. (2012) for other galaxies. 푓 Eﬀective radii taken from Sofue et al. (2009) for MW, van der Marel (2006) for LMC, Gonidakis et al. (2009) for SMC, Strickland et al. (2004) for NGC 253, and Jarrett et al. (2003) for M82 and NGC 2146.

1042 1042

observed NGC 2146 observed 41 Γ 41 Γ 10 our model ( inj=2.2) 10 our model ( inj=2.2) M82 ) ∝ ψ ) ∝ ψ Lγ M82 Lγ Mgas -1 -1 40 ∝ ψ1.58 40 ∝ ψ 0.99 10 Lγ NGC 253 10 Lγ ( Mgas) NGC 253 NGC 2146

1039 1039

MW MW 1038 M33 1038

(0.1-100 GeV) (erg s SMC (0.1-100 GeV) (erg s γ γ

L L M33 LMC LMC 1037 1037 SMC 1036 1036 10-1 100 101 10-2 10-1 100 101 102 ψ -1 ψ 9 2 -1 (Msun yr ) Mgas (10 Msun yr ) Figure 1. Gamma-ray luminosities of nearby galaxies predicted by our model, in comparison with the observed luminosities. The left panel is shown as a function of SFR, while the right panel as a function of SFR multiplied by gass mass. The solid lines are ﬁts by a proportional relation, 퐿훾(0.1–100 GeV) ∝ 휓 or 휓푀gas, but the dashed lines are ﬁts with a free power-law index. It should be noted that the gamma-ray energy range is 0.2–100 GeV for NGC 2146, while 0.1–100 GeV for all others.

If we assume the same 퐿훾 (1 TeV)/SFR ratio as NGC 253, we can catalog but whose expected TeV gamma-ray flux is brighter than relate TeV gamma-ray luminosities and SFRs as the CTA sensitivity limit (∼ 1 × 10−13 erg s−1 cm−2). We then add these galaxies to our sample to ensure that it definitely contains 퐿훾 (1 TeV) 휓 ∼ 9.1 × 1037 . (3) all galaxies that are potentially detectable by CTA. We note that / −1 erg s M⊙yr Centaurus A also satisfies this condition, but is not added to our The coefficient of this equation does not change significantly (within sample because it is well known that its gamma-ray emission is 20 % change) if we use M82 instead of NGC 253. We note that there dominated by its AGN activity (Aharonian et al. 2009; Abdo et al. can be galaxies that have higher 퐿훾 (1 TeV)/SFR ratios than NGC 2010e; H. E. S. S. Collaboration et al. 2020). 253. In the most optimistic scenario where cosmic-ray protons lose Among those added eight galaxies, M33 and NGC 2403 have all the energy to pp collisions, this ratio could be higher by a factor been already detected by Fermi (Xi et al. 2020b; Ajello et al. 2020). of about three, assuming the Salpeter IMF, the supernova mass Especially, NGC 2403 is interesting because its emission is decaying threshold of 8푀⊙, cosmic-ray energy of 1050 erg from a supernova, with time and this emission is coincident with SN 2004dj. However, and a gamma-ray spectral index of 2.2 above 0.1 GeV. If we use time variability is rather marginal, and to examine whether this this optimistic 퐿훾 (1 TeV)/SFR ratio to estimate TeV gamma-ray emission is really coming from a supernova, the estimate of steady luminosities, we find eight galaxies that are not in the KINGFISH gamma-ray flux from its star-forming activity is important.

MNRAS 000, 1–9 (2020) 4 Shimono et al.

NGC 253 M82 10-11 10-11

Fermi LAT (l,b)=(120°,45°) TS=25, 0.25 dex bin

) ) VERITAS 50h -1 H.E.S.S. 50h -1 σ

s σ s 5 , 0.2 dex bin 10-12 5 , 0.2 dex bin 10-12 -2 -2 (erg cm (erg cm γ γ /dE /dE γ -13 Γ γ -13 Γ 10 inj=2.0 10 inj=2.0 dF dF

γ 2.1 γ 2.1 E 2.2 E 2.2 2.3 2.3 2.4 2.4 Fermi Fermi H.E.S.S. VERITAS 10-14 10-14 10-4 10-3 10-2 10-1 100 101 102 10-4 10-3 10-2 10-1 100 101 102 Eγ (TeV) Eγ (TeV)

Figure 2. GeV–TeV spectra of NGC 253 (left) and M82 (right) predicted by our model, in comparison with the observed spectra (H. E. S. S. Collaboration et al. 2018 for NGC 253 and Ackermann et al. 2012b; VERITAS Collaboration et al. 2009 for M82). Sensitivities of Fermi and TeV telescopes are also shown. Sensitivities of TeV telescopes are for 5휎 detection by a 50 hr observation in a 0.2 dex photon energy bin, 1. Sensitivities for Fermi (Pass 8 Release 3 Version 2) is the ﬂux to gain TS = 25 in a 0.25 dex photon energy bin 2.

We need effective radii of galaxies to calculate gamma-ray in a photon energy bin of a 0.2 dex width, and a fainter flux can luminosities and spectra. We use the J-band half-light radii of the be detected if a wider energy bin width is adopted. In fact, NGC 2MASS Large Galaxy Atlas (Jarrett et al. 2003) for most galaxies 253 has been detected by H.E.S.S, whose flux is also fainter than in our sample. Effective radii of dwarf galaxies DDO 53, Ho I, and its sensitivity limit by a similar factor. Therefore we conclude that M81dwB are not available in the 2MASS data, and we use the results there is a reasonable chance of detection of these galaxies by CTA of Oh et al. (2011) for these galaxies. The physical parameters of if sufficient observing time is devoted. In Fig. 4 we also show the each galaxy are listed in Table 2. spectrum of NGC 2146, since it has been detected by Fermi. The TeV flux predicted by our model is lower than the top five galaxies, but our model flux is lower than the observed Fermi flux by a factor 4 RESULT of a few. The discrepancy is perhaps due to the limitation of our modeling, though the observational errors of the Fermi flux are 4.1 TeV gamma-ray detectability by CTA relatively large compared with other Fermi-detected galaxies. If the In Figure 3 (left), we show the predicted fluxes at 1 TeV by our TeV flux is also enhanced by the same factor from our prediction, there is a chance to detect this galaxy by CTA. model assuming Γinj = 2.2. In the plot, these fluxes are compared with the simple expectation using Equation 3. The fluxes predicted by our model are typically 10 times lower than the simple estimates, 4.2 Properties of TeV gamma-ray spectrum indicating that cosmic rays responsible for TeV emission are less confined than those in NGC 253. For comparison, the same plot The power-law index Γinj of injected proton spectrum is a free model is made for the Fermi energy band (3 GeV) as the right panel of parameter in our model, but the gamma-ray energy spectrum is the same figure, in comparison with the simple estimates being calculated by the model taking into account cosmic-ray propagation proportional to SFR: and escape. Then the difference between gamma-ray and proton spectra is a good indicator of the efficiency of cosmic-ray collisions 퐿훾 (3 GeV) 휓 ∼ . × 38 , with ISM before its escape. Therefore we show the histgram of 5 8 10 − (4) erg/s M⊙yr 1 훼 − Γinj in Figure 4.2, where 훼 is the photon spectral index defined −훼+1 where the coefficient is again determined based on NGC 253. The as 푑퐹훾/푑퐸훾 ∝ 퐸훾 . We calculated 훼 by a power-law fit to the fluxes predicted by our model are again lower than the simple es- model spectra in the range of 0.1–100 TeV. In most galaxies 훼 − Γinj timates, but the differences are smaller than the TeV band, which is larger than 0.2, but NGC 1482 and DDO 165 have notably smaller is reasonable because of stronger confinement expected for lower values than other galaxies, implying that cosmic-ray interaction is energy cosmic rays. particularly efficient in these. Table 3 presents gamma-ray fluxes (퐸훾 푑퐹훾/푑퐸훾 at 1 TeV) To examine this, we made a plot of 퐿(1 TeV)/휓 versus Σgas predicted by our model for the galaxies considered in this paper, (surface gas density) in Figure 6 (left panel). If Σgas is sufficiently in descending order when Γinj = 2.2. The spectra of the top five high, cosmic-ray collision efficiency would be high and gamma- galaxies (NGC 5236, M33, NGC 6946, IC 342, and NGC 7331) ray emission would be close to the calorimetric limit, and hence are shown in Figure 4. For simplicity, we compare our model fluxes 퐿(1 TeV)/휓 will become constant asymptotically. This trend is in- to the sensitivity of CTA South regardless of the positions of the deed seen in the figure, and NGC 1482 and DDO 165 are located galaxies on the celestial sphere, noting that the difference between at the highest Σgas region. The spectrum of NGC 1482 predicted by CTA North and South is modest (less than a factor of ∼3) for energies our model is shown in Figure 4 (bottom left). Comparing to the CTA below ∼ 10 TeV. The fluxes of these galaxies assuming Γinj = 2.2 sensitivity, detection may not be easy but not impossible depending are lower than the CTA sensitivity limit (50h, 5휎) by a factor of on model parameters and uncertainties. If detected, we predict that a few. It should be noted that the sensitivity limit quoted here is this galaxy would have a particularly hard spectrum compared with

MNRAS 000, 1–9 (2020) Prospects of newly detecting SFGs 5

Table 2. Physical parameters of galaxies in the sample of this work. The full table is available in supplementary material (online).

−1 9 9 name 퐷 (Mpc) ref 휓(M⊙ yr ) ref 푀gas (10 M⊙) ref 푀star (10 M⊙) ref 푅eﬀ (kpc) ref

NGC 5236 4.5 (1) 3 (2),(3) 17 (4) 49 (5) 3 (6) M33 0.84 (2) 0.37 (2),(3) 1.9 (7),(8),(9) 3.2 (5) 1.4 (6) NGC 6946 6.8 (10) 4.9 (11) 21 (4) 59 (11) 4.5 (6) IC 342 3.3 (10) 1.5 (11) 14 (4) 81 (11) 3.9 (6) NGC 7331 14 (10) 4.5 (11) 42 (4) 140 (11) 3.2 (6)

References: (1) Galametz et al. (2011), (2) Kennicutt et al. (2008), (3) Sanders et al. (2003), (4) Rémy-Ruyer et al. (2014), (5) Dale et al. (2009), (6) Jarrett et al. (2003), (7) Gratier et al. (2010), (8) Heyer et al. (2004), (9) Pilyugin et al. (2014), (10) Kennicutt et al. (2011), (11) Rémy-Ruyer et al. (2015), (12) Paturel et al. (2003), (13) Allison et al. (2014), (14) Israel (1997), (15) Leroy et al. (2008), (16) Moustakas et al. (2010), (17) Madden et al. (2013), (18) Oh et al. (2011)

10 12 10 11 ) ) 2 2 m m

CTA 5- Sensitivity (50 h, bin = 0.2 dex) c c 13

10 1 1 NGC 5236 10 12 s s

M33 g

g NGC 6946 M33

r NGC 5236 r 14 NGC 1482 IC 342 Fermi TS=25 Sensitivity (bin = 0.25 dex)

10 e e ( (

NGC 6946 Fermi TS=25 Sensitivity (bin = 0.25 dex) IC 342 ) ) NGC 2403 l C l T e e

A 13 d

d 10

15 5 o o

10 -

DDO 165 m m S

NGC 1482 NGC 2403 e r r n u u s i o o 16 t ( i (

10 v

14 i

t 10 V V y

e e ( 5 T G 0

h 1

17 3

10 ,

t t b i a a

n x

15 = DDO 165 = 10 y E

x E = 0 d d

18 .

y 2 /

10 /

x x d .1 F

1 F . e 0 0 x = d d

= ) y y E 10 19 E 10 16 10 19 10 18 10 17 10 16 10 15 10 14 10 13 10 12 10 16 10 15 10 14 10 13 10 12 10 11 E dF /dE at 1 TeV (L SFR) (erg s 1 cm 2) E dF /dE at 3 GeV (L SFR) (erg s 1 cm 2)

Figure 3. The ﬂuxes at 1 TeV (left) and 3 GeV (right) predicted by our model assuming Γinj = 2.2 are shown in the vertical axes, in comparison with the simpler prediction assuming 퐿훾 ∝ SFR and the 퐿훾/SFR ratio of NGC 253 shown in the horizontal axes. The CTA and Fermi sensitivity limits are the same as shown in Fig. 2.

−1 −2 Table 3. List of gamma-ray ﬂuxes (퐸훾 푑퐹훾/푑퐸훾 at 1 TeV) predicted by our model, in units of erg s cm in the descending order when Γinj = 2.2. The full table is available in supplementary material (online).

name Γinj = 2.0 Γinj = 2.1 Γinj = 2.2 Γinj = 2.3 Γinj = 2.4

NGC 5236 1.2 × 10−13 6.4 × 10−14 3.4 × 10−14 1.7 × 10−14 8.8 × 10−15 M33 1.1 × 10−13 6.1 × 10−14 3.2 × 10−14 1.7 × 10−14 8.5 × 10−15 NGC 6946 6.8 × 10−14 3.7 × 10−14 1.9 × 10−14 1.0 × 10−14 5.1 × 10−15 IC 342 5.9 × 10−14 3.2 × 10−14 1.7 × 10−14 8.7 × 10−15 4.4 × 10−15 NGC 7331 3.7 × 10−14 2.0 × 10−14 1.1 × 10−14 5.4 × 10−15 2.8 × 10−15

other SFGs. On the other hand, the predicted flux of DDO 165 is correlations between 퐿(3 GeV)/휓 versus Σgas or 푀gas are shown in far below the CTA sensitivity limit (see Figure 3). Figure 7. In both the energy bands, Σgas is a good indicator of 퐿훾/휓. Gamma-ray luminosities of SFGs are often compared with Compared with the relation in TeV, the relation in GeV becomes flat ≳ −2 휓푀gas, with an expectation of 퐿훾 ∝ 휓푀gas. Here, the amount of gas at Σgas 1 g cm . This is expected because GeV emission would mass is considered as an indicator of cosmic-ray collision efficiency. reach the calorimetric limit at lower Σgas. To examine this, a correlation plot between 퐿(1 TeV)/휓 and 푀gas is also shown in the right panel of Figure 6. The data points show a positive correlation similar to the case of the 퐿(1 TeV)/휓-Σ gas 5 DISCUSSION & CONCLUSIONS correlation, but as expected, the scatter is much larger because the information of galaxy sizes is not used. This indicates a limitation In this work, we calculated expected fluxes and spectra of TeV of using 휓푀gas as an indicator of gamma-ray luminosity. The same gamma rays from nearby SFGs, mainly included in the catalog of

MNRAS 000, 1–9 (2020) 6 Shimono et al.

NGC 5236 M33 10-11 10-11 CTA South 50h Fermi LAT (l,b)=(120°,45°) 5σ, 0.2 dex bin TS=25, 0.25 dex bin

-12 -12 ) 10 ) 10 -1 -1 s s -2 -2

10-13 10-13 (erg cm (erg cm γ γ /dE /dE γ Γ γ inj=2.0 dF dF γ 2.1 γ

E -14 E -14 10 2.2 10 2.3 2.4 Fermi 10-15 10-15 10-4 10-3 10-2 10-1 100 101 102 10-4 10-3 10-2 10-1 100 101 102 Eγ (TeV) Eγ (TeV)

NGC 6946 IC 342 10-11 10-11

-12 -12 ) 10 ) 10 -1 -1 s s -2 -2

10-13 10-13 (erg cm (erg cm γ γ /dE /dE γ γ dF dF γ γ

E 10-14 E 10-14

10-15 10-15 10-4 10-3 10-2 10-1 100 101 102 10-4 10-3 10-2 10-1 100 101 102 Eγ (TeV) Eγ (TeV)

NGC 7331 NGC 2146 10-11 10-11

-12 -12 ) 10 ) 10 -1 -1 s s -2 -2

10-13 10-13 (erg cm (erg cm γ γ /dE /dE γ γ dF dF γ γ

E 10-14 E 10-14

10-15 10-15 10-4 10-3 10-2 10-1 100 101 102 10-4 10-3 10-2 10-1 100 101 102 Eγ (TeV) Eγ (TeV)

NGC 1482 NGC 2403 10-11 10-11

-12 -12 ) 10 ) 10 -1 -1 s s -2 -2

10-13 10-13 (erg cm (erg cm γ γ /dE /dE γ γ dF dF γ γ

E 10-14 E 10-14

10-15 10-15 10-4 10-3 10-2 10-1 100 101 102 10-4 10-3 10-2 10-1 100 101 102 Eγ (TeV) Eγ (TeV)

Figure 4. Examples of gamma-ray spectra of nearby galaxies predicted by our model. NGC 5236, M33, NGC 6946, IC 342, and NGC 7331 are the brightest among the sample considered in this work (except those already detected in TeV). NGC 2146 is not in the top ﬁve, but has already been detected by Fermi. NGC 1482 is predicted to have a particularly hard spectrum which may be detected by CTA. NGC 2403 has been detected by Fermi, but the GeV ﬂux might originate from a supernova. Data points are taken from Xi et al. (2020b) for M33, Tang et al. (2014) for NGC 2146, and Xi et al. (2020a) for NGC 2403.

MNRAS 000, 1–9 (2020) Prospects of newly detecting SFGs 7

the TeV regime (Linden & Buckman 2018; Sudoh et al. 2019). If 40 future CTA observations detect SFGs with ﬂuxes larger than predicted by our hadronic model, it may suggest a contribution from 35 leptons, oﬀering support for the importance of pulsar emission in 30 the TeV sky.

20 ACKNOWLEDGEMENTS Number 15 TT was supported by the JSPS/MEXT KAKENHI Grant Numbers 18K03692 and 17H06362. T.S. is supported by a Research Fellow- 10 ship of Japan Society for the Promotion of Science (JSPS) and by JSPS KAKENHI Grant No. JP 18J20943. 5 NGC 1482 DDO 165 0 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 α Γ - inj REFERENCES Abdo A. A., et al., 2009, Phys. Rev. Lett., 103, 251101 Abdo A. A., et al., 2010a, A&A, 512, A7 Figure 5. Histogram of 훼 − Γinj assuming Γinj = 2.2, where 훼 is the power- Abdo A. A., et al., 2010b, A&A, 523, L2 law index of a photon spectrum, obtained by a fit to the gamma-ray spectra Abdo A. A., et al., 2010c, A&A, 523, A46 of model galaxies in 0.1–100 TeV. Abdo A. A., et al., 2010d, ApJ, 709, L152 Abdo A. A., et al., 2010e, ApJ, 719, 1433 Acero F., et al., 2009, Science, 326, 1080 KINGFISH, based on the four physical quantities of galaxies: SFR, Ackermann M., et al., 2012a, ApJ, 750, 3 gas mass, stellar mass, and effective radius. 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MNRAS 000, 1–9 (2020) 8 Shimono et al.

NGC 253 -1 -1 ) 10 M82 DDO 165 )) 10 NGC 253 M82 -1 -1 yr NGC 2146 yr

sun NGC 2146 NGC 1482 sum /M /M -1 -2 -1 -2 M33 10 M33 10

erg s SMC MW erg s

39 SMC 39 MW (10

LMC (10 ψ ψ LMC 10-3 10-3 (1 TeV)/ (1 TeV)/ γ γ L L

10-4 10-4 10-3 10-2 10-1 100 101 10-2 10-1 100 101 -2 9 Σ (g cm ) Mgas (10 Msun)

Figure 6. Correlation between 퐿훾 (1 TeV)/휓 and gas surface density (left), or gas mass (right), of nearby galaxies predicted by our model assuming Γinj = 2.2. Blue points are galaxies detected by TeV gamma-ray telescopes.

100 100 NGC 253 ) NGC 2146 M82 ) M82 NGC 2146

-1 -1 NGC 253 yr yr sun sun /M /M

-1 NGC 1482 -1 10-1 10-1 MW DDO 165 SMC

erg s erg s MW 39 LMC SMC 39 M33 LMC M33 (10 (10 ψ ψ 10-2 10-2 (3 GeV)/ (3 GeV)/ γ γ L L

10-3 10-3 10-3 10-2 10-1 100 101 10-2 10-1 100 101 -2 9 Σ (g cm ) Mgas (10 Msun)

Figure 7. The same as Fig. 6, but for luminosities at 3 GeV. Blue points are galaxies detected by Fermi. The data point for MW is based on Strong et al. (2010), showing the range between the highest and lowest luminosities of their models.

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This paper has been typeset from a TEX/LATEX ﬁle prepared by the author.

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