Comment on "Constraining the annihilating dark matter mass by the radio continuum spectral data of NGC4214 galaxy"
CComment on “Constraining the annihilating dark matter mass by the radiocontinuum spectral data of NGC4214 galaxy”
Volker Heesen ∗ and Marcus Br¨uggen † University of Hamburg, Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germany (Dated: Received 7 October 2020; accepted 19 November 2020)In their recent paper, Chan and Lee discuss an interesting possibility: radio continuum emissionfrom a dwarf irregular galaxy may be used to constrain upper limits on the cross section of annihilat-ing dark matter. They claim that the contributions from nonthermal and thermal emission can beestimated with such accuracy that one can place new upper limits on the annihilation cross section.We argue that the observations presented can be explained entirely with a standard spectrum andno contribution from dark matter. As a result, the estimated upper limits of Chan and Lee are atleast by a factor of 100 too low.
Annihilation from dark matter (DM) particles may bedetected in radio continuum searches of nearby galaxies.Searches so far have concentrated on dwarf spheroidalgalaxies because they have very little star formation andthus no contaminating emission at radio frequencies. Sofar, these searches have not provided any detection andupper limits on the radio flux density can be converted toupper limits on the annihilation cross section for variousannihilation channels [1].A different approach was used in Chan and Lee [2], whoanalysed the radio continuum spectrum of the dwarf ir-regular galaxy NGC 4214. Since this galaxy, as all dwarfirregular galaxies, is star-forming, there is contamina-tion from both thermal (free-free) and nonthermal (syn-chrotron) emission. In order to perform any meaningfulDM detection experiment, a prior is needed on the ex-pected radio continuum emission. The best establishedprior is the radio continuum-star formation (radio-SFR)relation. This relates the radio continuum luminosity tothe star-formation rate in a galaxy. Using the radio-SFRrelation is not an alternative method to the one used inChan and Lee [2] but necessary even when looking atsingle galaxies. As the radio-SFR relation, a close corol-lary of the radio-far-infrared relation, is one of the mostuniversal and tightest relations known in galaxies [3], ig-noring it in order to make claims about the detection ofDM is not justified.In dwarf irregular galaxies, H α emission is a very goodstar-formation tracer because their dust content is low.Independent of the distance, we expect a tight correla-tion between the radio continuum flux density and theH α flux. This correlation is presented in Fig. 1, whereNGC 4214 is consistent with the best-fitting relation.Hence, the radio continuum emission in NGC 4214 is en-tirely in agreement with the expected value for the givenstar-formation rate in this galaxy. Thus, as we wouldargue, this galaxy cannot provide any meaningful upperlimits for the DM annihilation cross section. The mainflaw in the analysis of Chan and Lee [2] is that they as- ∗ [email protected] † [email protected] sume the measured flux density with its uncertainty asthe prior for the expected flux density. Their assumeduncertainty is only the measured uncertainty in the ra-dio flux density. However, such an approach is only validif we do not expect any contribution from star formation.What really determines the uncertainty of the prior is theuncertainty in the radio-SFR relation.The radio continuum spectrum of NGC 4214 showsthe typically concave spectral shape one expects froma constant, nonthermal radio spectral index and an in-creasing thermal fraction at high frequencies. Using thethermal contribution from Srivastava et al. [5] S th =20( ν/ . − . mJy we can fit the data of Chanand Lee [2] (who adopted it from Srivastava et al. [5]) IC 10NGC 1569NGC 4214NGC 2366DDO 50
FIG. 1. The 6-cm radio flux density in dwarf irregular galax-ies as a function of the H α flux. The data can be fitted bya power-law with a slope of 0 . ± .
05 in accordance with alinear relation. The standard deviation is 0 .
18 dex as indi-cated by shaded region around the best-fitting line. As canbe seen, NGC 4214 is entirely consistent with the relation andno additional radio-emitting component is needed. As we ar-gue in the text, the radio flux density would have to be 8 × higher than what is observed to claim a 5- σ detection. A fewbrighter dwarf irregular galaxies are annotated. Data takenfrom Hindson et al. [4]. a r X i v : . [ a s t r o - ph . GA ] F e b adding the nonthermal contribution with S nt = (120 ± ν/ . − . ± . mJy with a reduced χ ν = 1 . et al. [5] cautionagainst using their 150- and 325-MHz flux densities, butthis does not change our conclusions. So the radio contin-uum spectrum can be entirely explained with a standardthermal and nonthermal spectrum without any contribu-tion from DM. This is in fact stated in Chan and Lee[2]. Hence, it is valid to study the 6-GHz ( λ σ DM detection signal.In principle, the flux densities have a typical error of 10percent. Following the argument in Chan and Lee [2],adding 50 percent to the flux density, as they do, wouldthen amount to a 5 σ detection of a DM annihilation sig-nal. This is shown in their Fig. 3. This is of coursenot correct. The significance of the DM signal does notin this case primarily depend on how accurately the fluxdensities are measured. The dominant uncertainty lies inthe expected radio luminosity for a given star-formationrate. Hence, what really determines the significance ofthe DM detection is the deviation from the radio-SFRrelation. More specifically, the uncertainty in the non-thermal synchrotron spectrum is the main uncertainty,since for the thermal part H α emission is an excellentproxy.Hindson et al. [4] showed that the uncertainty for theradio-SFR relation in dwarf irregular galaxies is only0 . ±
50 percent. Nevertheless, thatmeans that a 5 σ detection requires a deviation of 1 dex,equivalent to a factor of 10, from the radio-SFR rela-tion. A similar excess is needed for the flux densities as we show in Fig. 1. Only if such an excess is found, onecan start to speculate about additional emission mecha-nisms such as a signal from DM annihilation. In short,rather than changing the flux density of NGC 4214 by 50percent ( ≈
50 mJy) for a 5 σ detection, the flux densityneeds to increase by a factor of 10 ( ≈
900 mJy), a factorof nearly 20 larger. The upper limits for the annihila-tion cross section would increase by the same factor. Ofcourse, one would then still need to look for other sourcesof contamination such as from background radio galaxies,but we leave aside this complication for now.Another shortcoming of the analysis in star-formingdwarf irregular galaxies is that the cosmic-ray resi-dence time may be limited due to outflows and winds.For NGC 4214, Kepley et al. [6] estimate a residencetime of 10 Myr as indicated by the flat radio spec-tral index. The corresponding diffusion coefficient D =(1 kpc) / (10 Myr) is with D = 3 × cm s − a fac-tor of ∼
100 larger than what Chan and Lee [2] used intheir analysis. Even using a lower value of 10 cm s − would suppress the radio continuum luminosity by an-other factor of 10 since the cosmic-ray energy density issuppressed. Taken together, we estimate that the derivedupper limits of Chan and Lee [2] for the annihilation crosssection are by at least a factor of 100 too low.In summary, the complex relations that regulate theradio continuum emission in galaxies with star formationmean that they are not suitable for a DM search in theradio continuum. This is particularly the case for dwarfirregular galaxies that cannot hold on to their cosmic-rayelectrons. The resulting suppression of the synchrotronemission leads to an increased scatter of the nonthermalradio-SFR relation [4]. Better targets for a DM search aredwarf spheroidal galaxies, which lack this complication. ACKNOWLEDGMENTS
This work is supported by the Deutsche Forschungsge-meinschaft (DFG, German Research Foundation) underGermany’s Excellence Strategy – EXC 2121 QuantumUniverse – 390833306. [1] M. Vollmann, V. Heesen, T. W. Shimwell, M. J. Hard-castle, M. Br¨uggen, G. Sigl, and H. J. A. R¨ottgering, Ra-dio constraints on dark matter annihilation in Canes Ve-natici I with LOFAR, Mon. Not. R. Astron. Soc. , 2663(2020), arXiv:1909.12355 [astro-ph.HE].[2] M. H. Chan and C. M. Lee, Constraining the annihilatingdark matter mass by the radio continuum spectral data ofthe NGC4214 galaxy, Phys. Rev. D , 063017 (2020),arXiv:2009.09562 [astro-ph.HE].[3] M. S. Yun, N. A. Reddy, and J. J. Condon, Radio proper-ties of infrared-selected galaxies in the IRAS 2 Jy sample, Astrophys. J. , 803 (2001), arXiv:astro-ph/0102154[astro-ph].[4] L. Hindson, G. Kitchener, E. Brinks, V. Heesen, J. West-cott, D. Hunter, H.-X. Zhang, M. Rupen, and U. Rau,A radio continuum study of dwarf galaxies: 6 cm imag-ing of LITTLE THINGS, Astrophys. J. , 29 (2018),arXiv:1801.05348 [astro-ph.GA].[5] S. Srivastava, N. G. Kantharia, A. Basu, D. C. Srivastava,and S. Ananthakrishnan, GMRT radio continuum study ofWolf-Rayet galaxies - I. NGC 4214 and NGC 4449, Mon.Not. R. Astron. Soc. , 860 (2014), arXiv:1405.6913 [astro-ph.GA].[6] A. A. Kepley, E. G. Zweibel, E. M. Wilcots, K. E. John-son, and T. Robishaw, The magnetic field of the irreg- ular galaxy NGC 4214, Astrophys. J.736