Analysing the radio flux density profile of the M31 galaxy: a possible dark matter interpretation
aa r X i v : . [ a s t r o - ph . H E ] J a n Mon. Not. R. Astron. Soc. , 1–6 (XXXX) Printed 5 January 2021 (MN L A TEX style file v2.2)
Analysing the radio flux density profile of the M31 galaxy:a possible dark matter interpretation
Man Ho Chan ⋆ , Chu Fai Yeung , Lang Cui † , Chun Sing Leung Department of Science and Environmental Studies, The Education University of Hong Kong, Tai Po, Hong Kong, China Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi, China Hong Kong Polytechnic University, Hong Kong, China
Accepted XXXX, Received XXXX
ABSTRACT
Some recent studies have examined the gamma-ray flux profile of our Galaxy to de-termine the signal of dark matter annihilation. However, the results are controversialand no confirmation is obtained. In this article, we study the radio flux density profileof the M31 galaxy and show that it could manifest a possible signal of dark matterannihilation. By comparing the likelihoods between the archival observed radio fluxdensity profile data and the predicted radio flux density profile contributed by darkmatter and stellar emission, we can constrain the relevant dark matter parameters.Specifically, for the thermal annihilation cross section via the b ¯ b channel, the best-fitvalue of dark matter mass is ∼
30 GeV, which is consistent with the results of manyrecent studies. We expect that this method would become another useful way to con-strain dark matter, which is complementary to the traditional radio analyses and theother indirect detections.
Key words: (Cosmology:) dark matter; radio continuum: galaxies
In the past several decades, observational data of galaxiesand galaxy clusters revealed the existence of dark matter.For example, observations indicate that most galactic rota-tion curves are flat in the galactic outskirt regions, whichcontradict to the theoretical predictions based on the lu-minous mass distributions in galaxies. Also, the dynamicalmasses of most galaxy clusters probed from their hot gas dis-tributions are much larger than their total luminous masses.Therefore, many astrophysicists believe that a large amountof unknown particles called dark matter exist in the uni-verse. However, none of the particles in the Standard Modelcan satisfy the unique properties of dark matter - almost nointeraction with ordinary matter except gravity.Many theoretical models suggest that dark matterwould self-annihilate to give high-energy gamma rays, elec-trons, positrons and neutrinos. In particular, some re-cent analyses of gamma-ray and radio observations haveclaimed the discoveries of potential signals of annihilat-ing dark matter. For example, using the gamma-ray en-ergy spectrum of our Galaxy or some nearby globularclusters (e.g. 47 Tuc, Omega Centauri) observed fromthe Fermi-Large Area Telescope, some studies show that ⋆ [email protected] † [email protected] dark matter with mass m ≈ −
40 GeV annihilat-ing via the b ¯ b quark channel can best explain the ob-served spectral shapes (Daylan et al. 2016; Calore et al.2015; Abazajian & Keeley 2016; Cholis, Linden & Hooper2019; Brown et al. 2018, 2019). The constrained annihila-tion cross sections are surprisingly close to the thermal anni-hilation cross section h σv i ≈ . × − cm s − predictedby standard cosmology (Steigman, Dasgupta & Beacom2012).On the other hand, indirect detection of darkmatter using radio waveband is also good for con-straining dark matter parameters. For example, someearlier studies have used the radio data of our Galaxyto constrain dark matter (Blasi, Olinto & Tyler 2003;Aloisio, Blasi & Olinto 2004; Borriello, Cuoco & Miele2009). Later studies have started to focus on the MilkyWay satellite galaxies such as Large Magellanic Cloud(LMC) (Tasitsiomi, Siegal-Gaskins & Olinto 2004;Baltz & Wai 2004; Siffert et al. 2011), nearby galax-ies (e.g. M31 and M33 galaxies) (Borriello et al. 2010;Egorov & Pierpaoli 2013; Chan 2018) and galaxy clusters(Colafrancesco, Profumo & Ullio 2006; Chan et al. 2020b;Chan & Lee 2019, 2021) to search for dark matter signals.Some recent studies show that certain ranges of dark mattermass can give very good fits to the radio continuum spectraof some galaxy clusters (Chan & Lee 2019, 2021).In particular, most of the previous radio stud- © XXXX RAS
Chan et al. ies have used the total integrated radio emission flux(Blasi, Olinto & Tyler 2003; Aloisio, Blasi & Olinto 2004),radio intensity of certain ideal regions (Borriello et al.2010; Siffert et al. 2011) or total integrated radiofrequency (energy) spectrum (multi-frequency ap-proach) (Tasitsiomi, Siegal-Gaskins & Olinto 2004;Borriello, Cuoco & Miele 2009; Chan 2018) of a structureto constrain dark matter. Nevertheless, using the radialemission profile can also provide useful constraints for darkmatter. For example, some previous studies have shownthat the gamma-ray emissions in our Galactic Center tracethe dark matter density distribution, which provide anindirect potential evidence of dark matter annihilation(Daylan et al. 2016; Calore et al. 2015). However, on thecontrary, some later studies show that the gamma-rayemissions may probably trace the stellar density profilerather than the dark matter density profile (Bartels et al.2018). Therefore, whether the gamma-ray flux profilefollows the dark matter distribution in our Galactic Centerhas now become a controversial issue.Unfortunately, the resolution of gamma-ray telescopesis not high enough for us to analyse the central gamma-rayflux profiles of other extragalactic targets. Therefore, search-ing dark matter signals by using the gamma-ray flux profilesof other galaxies is very difficult. Nevertheless, current verylarge radio telescopes or radio interferometers can obtainradio data with a very high resolution and sensitivity. Theresolution can be as small as 10” so that we can observethe radio flux density profiles of galaxies or galaxy clusters.Therefore, radio flux density profile analysis can be used toserve as an independent and complementary study to searchfor dark matter annihilation signals. In view of this, however,not so much attention has been paid in considering the ra-dial emission profile (the functional form) in radio bands toconstrain dark matter. In this article, we use the radio fluxdensity profile of the M31 galaxy as an example to illustratehow this can be done. We show that some potential darkmatter annihilation signals can be manifested in the radioflux profile of the M31 galaxy. The best-fit value of m forthermal dark matter generally agrees with the popular rangesuggested by some gamma-ray studies. We revisit the archival radio data of the central region ofthe M31 galaxy reported in Gieߨubel & Beck (2014). Thedata were obtained by the combination of the Very LargeArray (VLA) and the Effelsberg radio telescope data, whichconsist of two different frequencies ( ν = 4 .
85 GHz and ν =8 .
35 GHz). The useful data cover sizes of the central region r . ν = 4 .
85 GHz) and r . ν = 8 . ◦ θ from the center. The angular dis-tance for each bin is taken as 26” (1 . × − rad), which isequivalent to 0.1 kpc at the M31 center (assuming distanceto the galaxy D = 785 kpc (Egorov & Pierpaoli 2013)). Asthere are fluctuations in the radio flux density for the sameangular radius, we take the 1 σ standard deviation as our ra-dio flux density profile uncertainties. Using this method, wecan get the radio flux profiles (radio flux density per beamsize against θ ) of the central region of the M31 galaxy fortwo radio frequencies (see Fig. 1). The solid angle of thebeam size is ∆Ω = 1 . × − sr. Dark matter annihilation would give a large amount ofhigh-energy electrons and positrons. These electrons andpositrons would emit synchrotron radiation in radio bandswhen there is a large magnetic field strength. The powerfor synchrotron emission (with energy E ) takes the follow-ing form (Aloisio, Blasi & Olinto 2004; Profumo & Ullio2010): P DM ( E, ν, ~r ) = √ e m e c B ( ~r ) F ( ν/ν c ) , (1)where ν c is the critical synchrotron frequency, B is the mag-netic field strength and F is the synchrotron kernel function.Beside synchrotron radiation cooling, the high-energyelectrons and positrons would also cool down via in-verse Compton scattering (ICS), Bremsstrahlung radiationand Coulomb loss (Colafrancesco, Profumo & Ullio 2006;Egorov & Pierpaoli 2013). In particular, synchrotron cool-ing and the ICS cooling would dominate at the M31 galacticcenter. Due to the very high cooling rate, most of the high-energy electrons and positrons produced from dark matterannihilation would quickly lose their energy before leavingthe central region. However, the actual diffusion length ofthe high-energy electrons and positrons depends on the dif-fusion models. For the outer part of a galaxy (e.g. outsidethe bulge region), the scale of the magnetic field irregulari-ties is comparable to the gyroradius r g of the electrons andpositrons. As a result, the effect of turbulent diffusion is im-portant so that the diffusion of the electrons and positronsis quite efficient in the outer part of a galaxy. Nevertheless,in the central region of a galaxy, the picture is much moreuncertain and the scale of magnetic irregularities would bemuch smaller. Therefore, the diffusion coefficient is signifi-cantly reduced (Regis & Ullio 2008). Like our Galaxy, thediffusion in the deep central region of the M31 galaxy can bewell described by the Bœhm diffusion model, which meansthat diffusion effect is not very significant (Regis & Ullio2008). The effective diffusion length of the Bœhm diffusionmodel can be estimated by the simple random walk model(Bœhm et al. 2004). The stopping distance of an electronwith energy 1 GeV is d s ∼ √ r g ct c ∼ t c ∼ sis the cooling time. Therefore, almost all of the electrons andpositrons emitted due to dark matter annihilation would beconfined in the central region.By considering the diffusion-cooling equation, as thediffusion term is not important, the equilibrium energy © XXXX RAS, MNRAS , 1–6 nalysing the radio flux density profile of the M31 galaxy: a possible dark matter interpretation spectrum of the high-energy electrons and positrons be-come (Borriello, Cuoco & Miele 2009; Storm et al. 2013;Egorov & Pierpaoli 2013): dn e dE = h σv i ρ DM m b ( E ) Z mE dN e dE ′ dE ′ , (2)where ρ DM is the density profile of dark matter, b ( E ) is thecooling rate and dN e /dE ′ is the injected energy spectrumdue to dark matter annihilation, which can be obtained nu-merically for different annihilation channels (Cirelli et al.2011). The radio emissivity contributed by dark matter anni-hilation is mainly determined by the peak frequency so thatthe line-of-sight synchrotron radiation flux density (the ra-dio flux density) within a solid angle ∆Ω can be simplified bycombining Eq. (1) and Eq. (2) with the monochromatic ap-proximation (Bertone et al. 2009; Profumo & Ullio 2010): S DM ≈ πν (cid:20) √ h σv i m (1 + C ) E ( ν ) Y ( ν, m ) (cid:21) Z ρ DM ds ∆Ω , (3)where s is the line-of-sight distance defined as r = √ D + s − Ds cos θ , Y ( ν, m ) = R mE ( ν ) ( dN e /dE ′ ) dE ′ and E ( ν ) = 14 . ν/ GHz) / ( B/µ G) − / GeV. Here, C is thecorrection factor of the ICS cooling contribution. The radia-tion density due to synchrotron cooling is ω B ≈ . .For the ICS radiation density, the value for the M31 galaxycentral region has not been well-determined. Nevertheless,we know that the value for the Milky Way centre is about ω i = 8 eV/cm (Egorov & Pierpaoli 2013). Also, the massof the M31 bulge is about 2.3 times of the mass of theMilky Way bulge (Bla˜na et al. 2018; Karukes et al. 2020).Therefore, assuming that they have similar luminosity-to-mass ratio, the ICS radiation density for the M31 galaxycentral region should be ω i ≈
19 eV/cm . Therefore, wehave C ≈ B = 15 − µ G for r = 0 . − B = 17 µ G, the energies at peak frequencies are E (4 .
85 GHz) = 7 . E (8 .
35 GHz) = 10 . h σv i = 2 . × − cm /s for m >
10 GeV if dark matter is thermally produced(Steigman, Dasgupta & Beacom 2012). We will first followthis standard paradigm to reduce our free parameters in fit-ting. As a result, S DM would be a function of ν , m and θ only. As the magnetic field strength is almost constant in the re-gion r = 0 . − . θ = 0 . − . ρ DM = ρ s r s /r (for small r ) as recent studiesshow that it can give a very good fit for the M31 galaxy rota-tion curve data with small uncertainties (Sofue 2015). Thedensity parameters are ρ s = (2 . ± . × − M ⊙ pc − and r s = (34 . ± .
1) kpc (Sofue 2015). The line-of-sightintegral in Eq. (3) is a function of the angular radius θ . For very small θ , it can be analytically written as (first-orderapproximation in θ ): I ( θ ) = Z ρ DM ds ≈ √ π Γ(3 / (cid:18) ρ s r s Dθ (cid:19) . (4)We fit the data with our dark matter model for variousannihilation channels. For each frequency ν , the dark mattermass m would be the only free parameter in the fitting.Generally speaking, the dark matter model can give good fitsfor the flux profile data for both frequencies. The goodnessof fits can be determined by the χ value, which is definedas χ = X i (cid:20) S m ( θ i ) − S o ( θ i ) σ o ( θ i ) (cid:21) , (5)where S m ( θ i ), S o ( θ i ) and σ o ( θ i ) are the data of the modeledflux density, observed flux density and uncertainties of theobserved flux density at different angular radii θ i . Specifi-cally, we find that the b ¯ b channel with m ∼
25 GeV cangive the best fit (i.e. smallest χ ) among all representativepopular annihilation channels ( χ = 7 .
1) (see Table 1 andFig. 2). We also separate the fit for each radio frequency.The corresponding χ values are 2.6 and 4.5 for 4.85 GHzand 8.35 GHz respectively.We also fit the data with the stellar model. We assumethat the normal astrophysical emissions such as pulsar emis-sions are tracing the stellar distribution. The stellar distri-bution in the bulge is commonly modeled by the Hernquistprofile (Sadoun, Mohayaee & Colin 2014): ρ b ∝ r ( r + r b ) , (6)where r b = 0 .
61 kpc for the M31 galaxy. The radio emis-sion due to conventional astrophysical processes (e.g. pulsaremissions) S ∗ is proportional to the stellar density profile.Therefore, we define the line-of-sight integral for the stel-lar radio emission as ˜ I ( θ ) = R [ r ( r + r b ) ] − ds and we canwrite S ∗ = k ˜ I ( θ ). The proportionality constant k is a freeparameter to fit the observed flux profile for each frequency.Since there are two different frequencies in the fits, we havetotally two free parameters for fitting. We find that the stel-lar model can give an overall better fit for the observed fluxprofiles ( χ = 3 .
2) compared with the dark matter model(see Table 1), especially for the profile of ν = 8 .
35 GHz( χ = 0 . S ∗ are shownin Fig. 3.Although the stellar model can give an overall betterfit compared with the dark matter model, one interestingfeature is that the dark matter model gives a better fit for the4.85 GHz data while the stellar model gives a better fit forthe 8.35 GHz. In fact, the radio emission due to dark matterannihilation via the b ¯ b channel would be more dominantin the low frequency regime because its energy spectrumhas a steeper spectral index. Our results might suggest thatconsidering both stellar model and dark matter model wouldbe able to get better fits for both data at 4.85 GHz and 8.35GHz.We consider the two-component model S DM + S ∗ tofit the observed flux profile data. By varying the free pa-rameters m and k , we find that a much better overall fitcan be obtained ( χ = 0 .
8) for m = 30 GeV (see Table 1).The radio flux profiles of the two-component model and the © XXXX RAS, MNRAS , 1–6
Chan et al. θ (radian)00.00020.00040.00060.00080.001 R a d i o f l ux d e n s it y p e r b ea m s i ze ( J y ) Figure 1.
The radio flux density profile data of the central re-gion of the M31 galaxy. The original radio map is taken fromGieߨubel & Beck (2014). corresponding components are shown in Fig. 4. Comparedwith the stellar model, the two-component model improvesthe overall fit with a 1 . σ statistical preference. Althoughit does not indicate a very large signal, including the darkmatter annihilation contribution can get an overall betterfit. The ratio of dark matter contribution to stellar contri-bution is approximately ranging from 1:1 to 3:1. Therefore,the central radio flux profile data of the M31 galaxy neithersimply trace the stellar profile nor the dark matter densityprofile, but better trace the stellar plus dark matter densityprofile.We have assumed the thermal annihilation cross section h σv i = 2 . × − cm s − in the above analysis. However, itis possible that dark matter was created non-thermally andthe cross section would be different from the standard value.Therefore, we release the cross section as a free parameterso that more general model-independent best-fit values ofcross section as a function of dark matter mass could be ob-tained. In Fig. 5, we plot the best-fit average dark matterannihilation cross section (via b ¯ b channel) against dark mat-ter mass ( m = 20 −
200 GeV) based on the two radio fluxdensity profile datasets (the black line), in which the best-fit χ values are same as that in the thermal dark matterscenario ( χ = 0 . σ margin. In Fig. 5,we also plot the 2 σ upper limit of the annihilation crosssection for m = 20 −
200 GeV (the red line). R a d i o f l ux d e n s it y ( J y / b ea m ) b quark channele + e - channel0 0.0005 0.001 0.0015 θ (Radian)00.00010.00020.00030.00040.00050.0006 Figure 2.
The radio flux density profiles of the dark matter anni-hilation model (upper: 8.35 GHz; lower: 4.85 GHz). Here m = 25GeV for the b ¯ b channel and m = 185 GeV for the e + e − channel. R a d i o f l ux d e n s it y ( J y / b ea m ) θ (Radian)00.00010.00020.00030.00040.00050.0006 Figure 3.
The radio flux density profiles of the stellar model(upper: 8.35 GHz; lower: 4.85 GHz).
Table 1.
The fitting properties for different models.Model Channel m χ χ χ (GeV) (4.85 GHz) (8.35 GHz) (both) S ∗ - - 2.9 0.2 3.2 S DM b ¯ b
25 2.6 4.5 7.1 e + e −
185 5.2 4.0 9.2 S DM + S ∗ b ¯ b
30 0.5 0.3 0.8 © XXXX RAS, MNRAS , 1–6 nalysing the radio flux density profile of the M31 galaxy: a possible dark matter interpretation R a d i o f l ux d e n s it y ( J y / b ea m ) Total flux profileStellar flux profileDM flux profile0 0.0005 0.001 0.0015 θ (Radian)00.00010.00020.00030.00040.00050.0006 Figure 4.
The radio flux density profiles of the two-componentmodel (upper: 8.35 GHz; lower: 4.85 GHz). Here we have assumed m = 30 GeV annihilating via the b ¯ b channel.
20 40 60 80 100 120 140 160 180 200m (GeV)1e-0271e-0261e-0251e-024 < σ v > ( c m s - ) best fit2 σ upper limit Figure 5.
The best-fit (black line) and the 2 σ upper limit (redline) of the annihilation cross section against dark matter mass.Here we have assumed dark matter annihilating via the b ¯ b chan-nel. In this article, we discuss an analysis of dark matter anni-hilation by using the central radio flux density profile of agalaxy. With the observed central radio flux density data ofthe M31 galaxy at two frequencies, we show that adding darkmatter contribution to the background radio emission dueto stellar component (the two-component model) can givean overall better fit for the data. The statistical preferenceof the two-component model is 1 . σ compared with the stel-lar model (the null hypothesis). Therefore, it reveals somepotential signal of dark matter annihilation. However, thedata and the available frequencies are quite limited so that the resulting flux density profiles have large uncertainties.We expect that a larger set of data with higher resolutionand more observing frequencies can provide a much betteranalysis to confirm the annihilation signal.In our analysis, with the thermal annihilation cross sec-tion, the best-fit m is ∼
30 GeV for the two-componentmodel (via b ¯ b channel). Surprisingly, this value and the an-nihilation channel is consistent with many recent studiesusing gamma-ray (Daylan et al. 2016; Brown et al. 2018,2019) and radio data (Chan & Lee 2021). We have as-sumed that the annihilation cross section follows the ther-mal annihilation cross section predicted by standard cos-mology (Steigman, Dasgupta & Beacom 2012). Therefore,thermally produced dark matter with mass ∼
30 GeV anni-hilating via b ¯ b channel has become one of the most probablesets of parameters for dark matter. Further observations andanalyses are required to confirm the above claim. Neverthe-less, if dark matter was not created thermally, a large rangeof best-fit dark matter mass is still possible to account forthe radio flux density profile of the M31 galaxy.Previous studies using gamma-ray data of our Galaxyhave performed similar analyses. Some studies claim thatthe gamma-ray flux profile traces dark matter distributionwhile other studies claim that the gamma-ray flux profiletraces stellar distribution. Therefore, it is still a controver-sial issue. However, the resolution of current gamma-raydetectors is not high enough to get the central gamma-rayflux profiles of other nearby galaxies. Fortunately, theresolution of current radio telescopes is able to fulfill thetask. If we can observe the radio flux density profiles ofsome nearby galaxies with high resolution and differentfrequencies, some better analyses or clearer signals could beobtained to verify our results. In fact, many previous radiostudies mainly focus on constraining dark matter by usingthe radio intensity of a region (e.g. radio intensity of M33galaxy or LMC, see Borriello et al. (2010); Siffert et al.(2011)) or radio frequency spectrum (multi-frequency ap-proach) (e.g. Tasitsiomi, Siegal-Gaskins & Olinto (2004);Chan (2018)) of galaxies or galaxy clusters. They couldidentify some ideal regions with the lowest signal to noiseratio for dark matter detection in the radio wavebands.Some other studies have obtained the radio sky map of ourGalaxy and used the sky map data to constrain dark matter(Borriello, Cuoco & Miele 2009). However, these studieshave not explicitly examined the likelihoods between theobserved radial emission profile and the predicted radialemission profile contributed by dark matter annihilation. Inour study, we show that using high resolution radio densityflux profile at the central region of a galaxy is good for con-straining dark matter. Therefore, observing and analysingthe radio flux density profile (i.e. the radial emission profile)would be another important way to detect the signal of darkmatter annihilation and constrain dark matter properties,which are complementary to the traditional radio analyses(using total integrated radio flux or frequency spectrum)(Blasi, Olinto & Tyler 2003; Aloisio, Blasi & Olinto2004; Tasitsiomi, Siegal-Gaskins & Olinto 2004;Borriello, Cuoco & Miele 2009; Chan 2018), cosmic-ray(including gamma-ray) analyses (Ackermann et al. 2015;Abdallah et al. 2016; Ambrosi et al. 2017; Aguilar et al.2019) and neutrino analyses (Albert et al. 2020) of darkmatter annihilation. © XXXX RAS, MNRAS , 1–6
Chan et al.
The work described in this paper was supported by a grantfrom the Research Grants Council of the Hong Kong Spe-cial Administrative Region, China (Project No. EdUHK28300518) and the Internal Research Fund from The Ed-ucation University of Hong Kong (RG 2/2019-2020R). LangCui thanks for the support from the National Key R&D Pro-gram of China (No. 2018YFA0404602), the National NaturalScience Foundation of China (NSFC grant No. 61931002 &U1731103) and the Youth Innovation Promotion Associationof the CAS (No. 2017084).
The data underlying this article will be shared on reasonablerequest to the corresponding author.
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