Galaxy Zoo: star-formation versus spiral arm number
Ross E. Hart, Steven P. Bamford, Kevin R.V Casteels, Sandor J. Kruk, Chris J. Lintott, Karen L. Masters
MMNRAS , 1–15 (2017) Preprint 13 November 2018 Compiled using MNRAS L A TEX style file v3.0
Galaxy Zoo: star-formation versus spiral arm number
Ross E. Hart, (cid:63) Steven P. Bamford, Kevin R.V. Casteels, Sandor. J. Kruk, Chris J. Lintott, Karen L. Masters School of Physics & Astronomy, The University of Nottingham, University Park, Nottingham NG7 2RD, UK Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 1A1, Canada Oxford Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK Institute for Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth PO1 3FX, UK
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Spiral arms are common features in low-redshift disc galaxies, and are prominent sitesof star-formation and dust obscuration. However, spiral structure can take many forms:from galaxies displaying two strong ‘grand design’ arms, to those with many ‘floccu-lent’ arms. We investigate how these different arm types are related to a galaxy’s star-formation and gas properties by making use of visual spiral arm number measurementsfrom Galaxy Zoo 2. We combine UV and mid-IR photometry from GALEX and WISEto measure the rates and relative fractions of obscured and unobscured star formationin a sample of low-redshift SDSS spirals. Total star formation rate has little depen-dence on spiral arm multiplicity, but two-armed spirals convert their gas to stars moreefficiently. We find significant differences in the fraction of obscured star-formation:an additional ∼ per cent of star-formation in two-armed galaxies is identified viamid-IR dust emission, compared to that in many-armed galaxies. The latter are alsosignificantly offset below the IRX- β relation for low-redshift star-forming galaxies. Wepresent several explanations for these differences versus arm number: variations in thespatial distribution, sizes or clearing timescales of star-forming regions (i.e., molecularclouds), or contrasting recent star-formation histories. Key words: galaxies: general – galaxies: spiral – galaxies: star formation – galaxies:structure
Spiral arms are common features in low-redshift galaxies,with as many as two-thirds of galaxies in the low-redshiftUniverse exhibiting spiral structure (Nair & Abraham 2010;Lintott et al. 2011; Willett et al. 2013). Spiral arms aresites of enhanced gas (e.g., Grabelsky et al. 1987; Engargiolaet al. 2003), star formation (e.g., Calzetti et al. 2005; Gros-bøl & Dottori 2012) and dust density (Holwerda et al. 2005)compared to the interarm regions of galaxy discs. The termspiral, however, encompasses a range of galaxies with vary-ing physical characteristics. To this end, spiral galaxies arecommonly described as either grand design, many-armed orflocculent (Elmegreen & Elmegreen 1982, 1987a). Grand de-sign spiral galaxies have two strong spiral arms propagatingthrough the entire disc, whereas many-armed or flocculentgalaxies associated with more fragmented spiral structure.In order to gain a complete understanding of the processes (cid:63)
E-mail: [email protected] that link spiral arms with star formation, star formation inall types of spiral galaxy must be considered.In the low-redshift Universe, overall star formation rates(SFRs) follow scaling relations with respect to galaxy stel-lar mass (Brinchmann et al. 2004; Salim et al. 2007) and gasdensity (Kennicutt 1998). The tightness of the relationshipbetween total SFR and stellar mass indicate that the pro-cesses responsible for star formation are regulated (Bouch´eet al. 2010; Lilly et al. 2013; Hopkins et al. 2014), and applyto all galaxies, irrespective of morphology. Further scalingrelations between SFR density and gas density within in-dividual galaxies (Kennicutt 1998; Leroy et al. 2008; Bigielet al. 2008) and of SFR with total gas mass (Saintonge et al.2016) indicate that the current SFR of low-redshift galaxiesis tied to the availability of gas to form new stars (Saintongeet al. 2013; Genzel et al. 2015), and that star formation ef-ficiency varies little within or between galaxies (Kennicutt1998; Saintonge et al. 2011).Spiral arms have been linked to enhanced star forma-tion as they are sites of increased density of young stars andgas in the Milky Way (Morgan et al. 1953; McGee & Milton © a r X i v : . [ a s t r o - ph . GA ] M a r Hart et al. ∼
1, and be subjectto swing amplification (Toomre 1964, 1981), be remnantsof recent tidal interactions (Sundelius et al. 1987; Dobbset al. 2010), or form via bar instabilities (Kormendy & Nor-man 1979). Many-armed or flocculent spiral patterns, how-ever, form via different mechanisms, and are more transient,short-lived structures in gas rich discs (e.g., Sellwood & Carl-berg 1984; Baba et al. 2013; D’Onghia et al. 2013). Giventhe little evidence for triggering of star formation by anyof these mechanisms, spiral arms appear to concentrate thestar-forming material into the arm regions. Star formationreflects the distribution of gas, but the arms do not affectthe overall star formation in the host galaxy (Vogel et al.1988; Elmegreen 2002; Moore et al. 2012).In this paper, the star formation and gas properties ofspiral galaxies are compared with respect to spiral arm num-ber. We use the visual classifications from Galaxy Zoo 2(GZ2; Willett et al. 2013) to define samples of spiral galaxiesdifferentiated by arm number (Hart et al. 2016). These arecompared by combining estimates of SFRs measuring unob-scured ultraviolet (UV) emission and obscured mid-infrared(MIR) emission. Atomic gas fractions are also compared toinvestigate whether the presence of different types of spiralstructure lead to deviations in star formation efficiency.This paper is organised as follows. In Section 2, the sam-ple selection and galaxy data are described. In Section 3, theSFR and gas properties of galaxies with different numbers ofspiral arms are compared. The results and their implicationswith respect to relevant theoretical and observational litera-ture are discussed in Section 5. The results are summarisedin Section 5.This paper assumes a flat cosmology with Ω m = . and H = − Mpc − . All galaxy morphological information is obtained from thepublic data release of GZ2 (Willett et al. 2013). As thispaper concerns the detailed visual morphologies of spiralgalaxies, we make use of the updated visual classificationsgiven in Hart et al. (2016), which are designed to give moreconsistent classifications for the multiple-answer questions in GZ2, such as spiral arm number. The galaxies classi-fied in GZ2 were taken from the SDSS main galaxy sample,which is an r -band selected sample of galaxies in the legacyimaging area targeted for spectroscopic follow-up (Strausset al. 2002). The Hart et al. (2016) sample contains all well-resolved galaxies in SDSS DR7 (Abazajian et al. 2009) to alimiting magnitude of m r ≤ . . In this paper, we considergalaxies classified in the normal-depth (single-epoch) DR7imaging with spectroscopic redshifts. Spectroscopic redshiftsare required for galaxies to have accurate morphological datacorrected for redshift-dependent classification bias (see Bam-ford et al. 2009 and Hart et al. 2016), to allow for accurate / V max corrections to the data (see Sec. 2.2), and for accuratemeasurements of rest frame photometry.Rest-frame absolute u g riz magnitudes for are obtainedfrom the NASA Sloan Atlas (NSA; Blanton et al. 2011).This restricts our sample to redshifts below 0.055, whichalso ensures our morphological information is robust. A low-redshift limit of z ≥ . is also applied to remove any galax-ies with large angular sizes, which may have associated mor-phological, spectroscopic and photometric complications. Intotal, there are 62,903 NSA galaxies in the redshift range . ≤ z ≤ . which were visually classified in GZ2.In order to study the star formation properties of thegalaxies in the sample, photometric data in the UV and IRare required. UV absolute magnitudes are obtained from theGALEX GR6 catalogue (Martin et al. 2005), which are alsoincluded in the NSA. Near-IR (NIR) and mid-IR (MIR) pho-tometry are from the AllWISE catalogue of galaxies from theWISE mission (Wright et al. 2010), and obtained from thereduced catalogue of Chang et al. (2015). We only matchWISE detections to galaxies where there is only one WISEsource within 6 (cid:48)(cid:48) of a galaxy, in line with Donoso et al.(2012), Yan et al. (2013) and Chang et al. (2015), and withminimum SNR > full sample .Galaxy stellar masses are obtained from the SDSS-WISESED fitting of Chang et al. (2015) for all galaxies in the fullsample .To investigate the gas properties of the galaxies in the full sample , we use measured gas masses from the α datarelease of the ALFALFA survey (Giovanelli et al. 2005;Haynes et al. 2011). We select reliable HI detections usingobjects with ALFALFA detcode=1 or 2 (described in Hayneset al. 2011) and a single SDSS matched optical counterpartin our full sample within the redshift range . ≤ z ≤ . .Due to the restrictions on the α -SDSS footprint and theimposed limiting redshift of z ≤ . , 20,024 galaxies fromthe full sample are targeted by ALFALFA and 5,570 of thosegalaxies have reliable H i fluxes. The GZ2 parent sample has an apparent magnitude limit of m r < . . The corresponding limit in absolute magnitude at z = . is M r = − . . This luminosity-limited sample is The GZ2 classifications are available fromhttp://data.galaxyzoo.org/. MNRAS , 1–15 (2017) tar-formation versus arm number − − − − − − − M r (a) M r -limited ( N gal =31002)Full sample ( N gal =45192) l og ( M ∗ / M (cid:12) ) (b) M ∗ -limited ( N gal =25063)Full sample ( N gal =45192) .
02 0 .
03 0 .
04 0 . redshift . . . . . l og ( M H I / M (cid:12) ) (c) M HI -limited ( N gal =2121)All α matches ( N gal =5570) Figure 1. (a) Plot of absolute magnitude vs. redshift for the fullsample of galaxies. The curved blue line indicates the luminositylimit as a function of redshift. Galaxies enclosed within the bluebox make up the luminosity-limited sample . (b) Stellar mass dis-tribution of the full sample vs. redshift. The curved line shows thecalculated stellar mass completeness limit and galaxies. Galaxiesin the red boxed region are included in the stellar mass-limitedsample . (c) Gas mass vs. redshift for all galaxies matched in α full sample . The curved line shows the calculated H i masscompleteness limit and galaxies. Galaxies in the green boxed re-gion are included in the H I mass-limited sample . indicated by the blue box of Fig. 1(a). The limit above whichthe sample is complete for a given stellar mass changes as afunction of redshift according to: log ( M ∗ , lim ) = .
17 log ( z ) + . , (1)which is indicated by the curved line of Fig. 1(b). The sampleis still incomplete for the reddest galaxies at log ( M ∗ / M (cid:12) ) < . . We therefore define a stellar mass-limited sample ofgalaxies, which includes all galaxies with M r ≤ − . and log ( M ∗ / M (cid:12) ) ≥ . . The limits of the sample are indicatedby the red box region in Fig. 1(b), and it includes 25,063galaxies in total.Similar completeness limits apply to the ALFALFAdata: at a given redshift, the sample is incomplete for theleast luminous H i sources. For a source of profile width 200 kms − ALFALFA has a 5 σ completeness limit of S lim ≥ . (Giovanelli et al. 2005), where S is the H i flux density. AL-FALFA fluxes are converted to gas masses using the follow-ing equation (Giovanelli et al. 2005): M H i = . × D S Jykms − , (2) and the estimated completeness limit at a given distance cantherefore be described by: log ( M H i , lim ) = . × ( . × D ) . (3)The limiting H i mass with redshift is shown by thecurved green line of Fig. 1(c). As many of the galaxies in α
70 are targeted, yet undetected, an H i upper limit can bemeasured for a galaxy at given distance using Eq. 3.Having defined the galaxy samples, a set of spiral galax-ies are selected using the visual statistics of GZ2. Galaxieswith p features or disc × p not edge on × p spiral > . and N spiral ≥ areselected in accordance with Hart et al. (2016). In this paper,we wish to test how star formation properties vary with re-spect to the spiral structure rather than any other morpho-logical differences. We therefore also exclude any stronglybarred spiral galaxies, which have p bar > . . Masters et al.(2010) used a similar cut to identify strongly barred galaxiesin GZ2. An axial ratio cut of ( b / a ) g > . is also imposed,where a and b are the SDSS DR7 g -band isophotal minorand major axis radii. This selection is used to ensure weonly select face on galaxies, to avoid contamination of mis-classified galaxies and to limit the amount of reddening dueto inclination. This was the same cut used in Masters et al.(2010) to identify reliable bar structures in discs. We haveverified that our arm number vote fractions are consistentwith inclination above this threshold. Each galaxy is thenassigned a spiral arm number, depending on which of theresponses to the arm number question in GZ2 had the high-est vote fraction. The number of galaxies for each of the armnumber subsamples that are included in the full sample , stel-lar mass-limited sample and with H i detections are given inTable 1.In this paper, we make use of the stellar mass-limitedsample to compare samples of galaxies with different spi-ral arm numbers. As galaxy SFR is related to total stellarmass (e.g., Brinchmann et al. 2004; Salim et al. 2007; Guoet al. 2013), our samples must be consistent in total stel-lar mass to ensure that any differences in star formationproperties are due to the morphological properties studiedin this paper. A boxplot for each of the stellar mass distri-butions is shown in Figure. 2. Here we see that the stellarmass distributions of each of the samples is consistent. The m = sample has median stellar mass of . M (cid:12) , whereasthe m = , and + samples have medians of . M (cid:12) , . M (cid:12) and . M (cid:12) . The only sample with a signif-icantly higher median stellar mass is the m = sample,where the corresponding value is . M (cid:12) . However, thisis the sample with the fewest galaxies (224), and the differ-ence is still much less than the overall spread in the data(the 84th-16th percentile range for all galaxies in the stellarmass-limited sample is ∼ . dex). We therefore elect to keepall galaxies in the stellar mass-limited sample of spirals, asthere is no significant stellar mass dependence on spiral armnumber. H α derived SFRs are obtained from MPA-JHU measure-ments of SDSS spectra (Brinchmann et al. 2004; Salim et al.2007), corrected for absorption using the Balmer decrementand for aperture effects using estimates derived from photo-metric galaxy colour gradients. Reliable H α measurements MNRAS000
70 are targeted, yet undetected, an H i upper limit can bemeasured for a galaxy at given distance using Eq. 3.Having defined the galaxy samples, a set of spiral galax-ies are selected using the visual statistics of GZ2. Galaxieswith p features or disc × p not edge on × p spiral > . and N spiral ≥ areselected in accordance with Hart et al. (2016). In this paper,we wish to test how star formation properties vary with re-spect to the spiral structure rather than any other morpho-logical differences. We therefore also exclude any stronglybarred spiral galaxies, which have p bar > . . Masters et al.(2010) used a similar cut to identify strongly barred galaxiesin GZ2. An axial ratio cut of ( b / a ) g > . is also imposed,where a and b are the SDSS DR7 g -band isophotal minorand major axis radii. This selection is used to ensure weonly select face on galaxies, to avoid contamination of mis-classified galaxies and to limit the amount of reddening dueto inclination. This was the same cut used in Masters et al.(2010) to identify reliable bar structures in discs. We haveverified that our arm number vote fractions are consistentwith inclination above this threshold. Each galaxy is thenassigned a spiral arm number, depending on which of theresponses to the arm number question in GZ2 had the high-est vote fraction. The number of galaxies for each of the armnumber subsamples that are included in the full sample , stel-lar mass-limited sample and with H i detections are given inTable 1.In this paper, we make use of the stellar mass-limitedsample to compare samples of galaxies with different spi-ral arm numbers. As galaxy SFR is related to total stellarmass (e.g., Brinchmann et al. 2004; Salim et al. 2007; Guoet al. 2013), our samples must be consistent in total stel-lar mass to ensure that any differences in star formationproperties are due to the morphological properties studiedin this paper. A boxplot for each of the stellar mass distri-butions is shown in Figure. 2. Here we see that the stellarmass distributions of each of the samples is consistent. The m = sample has median stellar mass of . M (cid:12) , whereasthe m = , and + samples have medians of . M (cid:12) , . M (cid:12) and . M (cid:12) . The only sample with a signif-icantly higher median stellar mass is the m = sample,where the corresponding value is . M (cid:12) . However, thisis the sample with the fewest galaxies (224), and the differ-ence is still much less than the overall spread in the data(the 84th-16th percentile range for all galaxies in the stellarmass-limited sample is ∼ . dex). We therefore elect to keepall galaxies in the stellar mass-limited sample of spirals, asthere is no significant stellar mass dependence on spiral armnumber. H α derived SFRs are obtained from MPA-JHU measure-ments of SDSS spectra (Brinchmann et al. 2004; Salim et al.2007), corrected for absorption using the Balmer decrementand for aperture effects using estimates derived from photo-metric galaxy colour gradients. Reliable H α measurements MNRAS000 , 1–15 (2017)
Hart et al. m . . . . l og ( M ∗ / M (cid:12) ) Figure 2.
Stellar mass distributions (using the measurements ofChang et al. 2015) for each of the arm number subsamples fromthe stellar mass limited sample . The boxes show the 25th quartile,75th quartile and the mean, and the vertical lines indicate theextent of the 5th and 95th percentiles.Morphology Full sample M ∗ -limited α detectedAll 45192 25063 5570Spiral 6333 3889 1792 m =
482 224 106 m = m = m =
534 357 165 m = +
756 550 271
Table 1.
Sample sizes for each of the samples defined in Sec. 2.2. rely on spectra averaged across entire galaxies, which are notavailable from SDSS data alone (the SDSS fibre size is 3 (cid:48)(cid:48) in diameter; the median r -band Petrosian aperture diame-ter of galaxies in our stellar mass-limited sample is 7.6 (cid:48)(cid:48) ). Inorder to account for this, the MPA-JHU catalogue appliesa correction to the fibre measured H α flux using photome-try measured outside the fibre (Salim et al. 2007), and thusprovide reliable total SFRs of star-forming galaxies (Salimet al. 2016).Alternatively, one can measure the SFRs of galaxies us-ing galaxy photometry rather than spectra. The UV andthe MIR are usually the wavelength ranges of choice, asthey are both dominated by emission from bright, youngstars. The UV continuum is almost completely flat (Kenni-cutt 1998), and arises from the direct photometric emissionof the youngest stellar population. We use the conversionfactor of Buat et al. (2008, 2011) to measure unobscuredSFRs: SFR
FUV = − . ( L FUV / L (cid:12) ) . (4)In order to get a reliable measure of SFR, however, theamount of UV emission that is obscured by dust must becorrected for. As dust absorbs UV photons and re-emits theenergy at longer wavelengths, then one can also measurethe SFR using the mid-infrared (MIR) emission. We use thefollowing prescription from Jarrett et al. (2013): SFR = ( − η ) − . ( L / L (cid:12) ) , (5)where L is the luminosity measured in the WISE µ m band, and η is the fraction of MIR emission that originates from the absorption of radiation from the older stellar popu-lation. Here, we use η = . measured in Buat et al. (2011).This conversion is for a Kroupa (2001) IMF, which we con-vert to a Chabrier (2003) IMF by adjusting the SFR by − . dex as suggested in Zahid et al. (2012) and Speagleet al. (2014). To reliably measure the total SFR, the µ m -derived SFR is then be added to the unobscured FUV mea-sured SFR (e.g., Wang & Heckman 1996; Heckman et al.1998; Hao et al. 2011; Jarrett et al. 2013; Clark et al. 2015): SFR total = SFR
FUV + SFR . (6)The specific star formation rate is given by sSFR = SFR total / M ∗ .To check the reliability of the SFRs obtained from thismeasure and to ensure our results are consistent with Wil-lett et al. (2015), we compare the SFRs from Eq. 6 with theMPA-JHU H α estimates in Fig. 3. The plot shows all galax-ies in the redshift range . < z ≤ . which have SNR > in both the GALEX FUV and the WISE µ m . The GALEXFUV band is complete for galaxies with L FUV ≥ . L (cid:12) at z = . and L FUV ≥ . L (cid:12) at z = . . The WISE µ m band is complete for galaxies with L FUV ≥ . L (cid:12) at z = . and L FUV ≥ . L (cid:12) at z = . . There is good agreementbetween the FUV+MIR derived SFRs and those inferredfrom the Balmer lines, with Pearson’s r coefficient of . ,indicative of a strong linear correlation between the vari-ables. The scatter is . dex. There is also no significantoffset between the measurements (the median difference is < . dex), suggesting that these SFR measurements areindeed comparable. We do however see galaxies at the lowerend of SFR
MPA − JHU with higher SFRs measured from Eq. 6.Salim et al. (2016) attributes galaxies with higher SFRs mea-sured in Chang et al. (2015) to galaxies with low measuredfluxes in WISE being overestimated. However, we do notexpect this effect to dominate as we find strong agreementbetween the SFR indicators using a single value of η = . from Buat et al. (2008), with the only differences observedfor galaxies with low SFRs ( (cid:46) . (cid:12) yr − ). This issue af-fects only a small fraction of galaxies in the sample, with < per cent of galaxies having more than . dex disagree-ment between the two SFR measures. We therefore elect tokeep all galaxies with SNR > in both the GALEX FUVand the WISE µ m in the sample of galaxies with reliablymeasured SFRs. In this section, we use the galaxy SFRs described in Sec. 2.3to investigate how the galaxy star formation properties ofour GZ2 galaxies vary with respect to spiral arm number.The FUV+MIR SFR measurements give a measure of SFRobtained from across the entire galaxy, and are thus sensi-tive to any SFR differences in the discs of galaxies. Theyalso give an opportunity to assess the relative fractions ofobscured and unobscured star formation directly, which willbe investigated in Sec. 3.2.
MNRAS , 1–15 (2017) tar-formation versus arm number − . − . . . . SFR
FUV + SFR ) − . − . . . . l og ( S F R M P A − J HU ) scatter = 0 . r p = 0 . Figure 3.
SFRs from Eq. 6 compared to the values measuredfrom the MPA-JHU catalogue (Brinchmann et al. 2004) for galax-ies in the redshift range . < z ≤ . with SNR > in theGALEX FUV and WISE µ m bands. The shaded grey contoursshow the regions enclosing 20, 40, 60 and 80% of the data points,and the thinner black line shows the expected one-to-one rela-tionship. The star formation main sequence (SFMS) describes theSFR of the galaxy population as a function of stellar mass. Inthe low-redshift Universe, this correlation has been shown tobe very tight for normal star-forming galaxies (Brinchmannet al. 2004; Salim et al. 2007; Chang et al. 2015). Galax-ies with significantly enhanced star formation are usuallyassociated with merging or interacting systems (Sanders &Mirabel 1996; Veilleux et al. 2003; Engel et al. 2010; Kavi-raj 2014; Willett et al. 2015), with the rest of the differenceacross the main sequence attributable to differences in thegas content and star formation efficiency of galaxies (Sain-tonge et al. 2011, 2016).In order to test whether the morphology of any of ourgalaxies affect the total star formation rate, the SFMS isplotted using the definition of sSFR defined in Sec. 2.3. Weelect to plot sSFR rather than SFR, as this more clearlydemonstrates how efficiently gas is converted to stars in star-forming galaxies with respect to stellar mass, M ∗ . Galaxiesat low-redshift can be considered bimodal in terms of theircolour and SFR properties (Baldry et al. 2006; Schawinskiet al. 2014; Morselli et al. 2016). To plot the SFMS, we musttherefore first select a set of galaxies that are consideredstar-forming. We choose to use the definition of Chang et al.(2015), which defines star-forming galaxies using SDSS ugriz photometry. Using this definition, we select galaxies with ( u − r ) rest < . or ( u − r ) rest < . ( r − z ) rest + . as star-forming. The majority of spiral galaxies (78.3 per cent) arefound to be star-forming using this method. The resultingplot of log ( M ∗ ) vs. log ( sSFR ) is shown in Fig. 4. As expected,we see a tight relationship, as galaxies with greater stellarmasses have lower sSFRs. The best-fit linear model to the . . . . . . M ∗ /M (cid:12) ) − . − . − . − . s S F R t o t a l ( y r − ) Star-forming galaxies ( N gal = 5296 ) sSFR = − . M ∗ − . Figure 4.
Stellar mass vs. sSFR for star-forming galaxies in theredshift range . < z ≤ . The grey contours show regionsenclosing 20, 40, 60 and 80 per cent of the points. The blue lineindicates the linear best fit line to the data. The black dashedvertical line indicates the galaxy of lowest stellar mass in thissample. data is given by: log ( sSFR expected ) = − .
49 log ( M ∗ / M (cid:12) ) − . , (7)and the scatter is . dex. This relationship can now be usedto assess whether galaxies have systematically high or lowsSFRs for their given M ∗ . We do this by defining the best-fitline as the expected sSFR for a galaxy of a given stellar mass.Given this information, we define the sSFR residual in Eq. 8: log ( sSFR residual ) = log ( sSFR total ) − log ( sSFR expected ) , (8)where log ( sSFR expected ) is given in Eq. 7. If a given galaxylies above the sSFR expected line, it has a higher sSFR forits stellar mass compared to the total star-forming galaxypopulation, and a positive value for sSFR residual . Conversely,galaxies below the line can be considered as being deficientin sSFR, and have a negative value for sSFR residual .Using equations 7 and 8, the effect that spiral galaxymorphology has on the total sSFRs of galaxies is now con-sidered. For this analysis, we use a subsample of spiral galax-ies, which we split into arm number subsamples , using themorphology criteria described in Sec. 2.2. We consider onlygalaxies taken from the stellar mass-limited sample , as thesegalaxies are well matched in stellar mass (see Sec. 2.2).As discussed in Sec. 2.3, we impose cuts in SNR to en-sure that we have flux measurements that are not dominatedby noise to get a reliable estimate of SFR in both the FUVand the MIR. It is therefore important to first check thecompleteness of each of the samples that we compare. Thefraction of galaxies that meet the minimum SNR > thresh-old in the GALEX FUV filter, the WISE µ m filter, andboth filters, are shown in Fig. 5. The overall completenessof each of the samples is similar, with ∼ – per cent ofgalaxies having a detection in both filters. We do see thatthe many-armed samples ( m = , or + ) have a greaterfraction of galaxies with reliable fluxes in both the µ m and the GALEX FUV than the m = and m = sample,however. Thus, galaxies with one or two spiral arms are morelikely to have undetectable MIR or FUV emission and thuslow SFRs. MNRAS000
49 log ( M ∗ / M (cid:12) ) − . , (7)and the scatter is . dex. This relationship can now be usedto assess whether galaxies have systematically high or lowsSFRs for their given M ∗ . We do this by defining the best-fitline as the expected sSFR for a galaxy of a given stellar mass.Given this information, we define the sSFR residual in Eq. 8: log ( sSFR residual ) = log ( sSFR total ) − log ( sSFR expected ) , (8)where log ( sSFR expected ) is given in Eq. 7. If a given galaxylies above the sSFR expected line, it has a higher sSFR forits stellar mass compared to the total star-forming galaxypopulation, and a positive value for sSFR residual . Conversely,galaxies below the line can be considered as being deficientin sSFR, and have a negative value for sSFR residual .Using equations 7 and 8, the effect that spiral galaxymorphology has on the total sSFRs of galaxies is now con-sidered. For this analysis, we use a subsample of spiral galax-ies, which we split into arm number subsamples , using themorphology criteria described in Sec. 2.2. We consider onlygalaxies taken from the stellar mass-limited sample , as thesegalaxies are well matched in stellar mass (see Sec. 2.2).As discussed in Sec. 2.3, we impose cuts in SNR to en-sure that we have flux measurements that are not dominatedby noise to get a reliable estimate of SFR in both the FUVand the MIR. It is therefore important to first check thecompleteness of each of the samples that we compare. Thefraction of galaxies that meet the minimum SNR > thresh-old in the GALEX FUV filter, the WISE µ m filter, andboth filters, are shown in Fig. 5. The overall completenessof each of the samples is similar, with ∼ – per cent ofgalaxies having a detection in both filters. We do see thatthe many-armed samples ( m = , or + ) have a greaterfraction of galaxies with reliable fluxes in both the µ m and the GALEX FUV than the m = and m = sample,however. Thus, galaxies with one or two spiral arms are morelikely to have undetectable MIR or FUV emission and thuslow SFRs. MNRAS000 , 1–15 (2017)
Hart et al. m . . . . f d e t ec t e d SNR
FUV ≥ SNR µ m ≥ SNR
FUV , µ m ≥ Figure 5.
Fraction of galaxies with
SNR > detection in theGALEX FUV (blue circles), WISE µ m (red squares), and both(black triangles), for each of the arm number subsamples takenfrom the stellar mass-limited sample of spiral galaxies. The error-bars show the σ errors, calculated using the method of Cameron(2011). The resulting distributions of sSFR residual for each of the arm number subsamples are shown in Fig. 6. Only galax-ies with reliable SNR > µ m are included in these distributions(the fractions that meet these requirements for each armnumber subsample are shown in Fig. 5). It is immediatelyapparent that there is no strong dependence of sSFR residual on spiral arm number – the median of the m = distribu-tion compared with the m = , , + distributions shift by (cid:46) . dex, which is much smaller than the scatter in theSFMS of . dex. This result is perhaps surprising, giventhat in Hart et al. (2016) it was shown that the many-armedsamples are much bluer in colour compared to their two-armed counterparts, an effect which was suggested to berelated to the star formation properties of the galaxies. The m = sample of spiral galaxies has the highest median valueof sSFR residual of . ± . , and is the only sample whichlies above the defined SFMS, although this is arm numbersubsample with the lowest number of galaxies with reliableFUV and 22 µ m measurements (148 galaxies). These highsSFRs are likely because GZ2 classified m = spiral galaxiesare associated with tidally induced features (Casteels et al.2013), which are in turn associated with enhanced star for-mation (Sanders & Mirabel 1996; Veilleux et al. 2003; Engelet al. 2010). This result is also expected, as Willett et al.(2015) showed that spiral arm number does not affect theposition of the SFMS, albeit using the spectroscopic SFRs ofBrinchmann et al. (2004). Merger systems on the other handdid show SFRs above the SFMS. It should also be noted thateach of the galaxy distributions lie very close to the SFMS:we make no cut in only selecting star-forming galaxies forthis analysis, yet the medians of each of the spiral galaxysubsamples are within (cid:46) . dex of the SFMS. Although asignificant number of galaxies are observed to be passivelystar-forming, (Masters et al. 2010; Fraser-McKelvie et al.2016), this population cannot be attributed to galaxies of aspecific spiral arm number – the majority of galaxies with any spiral arm number are actively star-forming. . . . n o r m a li s e dd e n s i t y m =1 ( N gal =148) . . . n o r m a li s e dd e n s i t y m =2 ( N gal =1341) . . . n o r m a li s e dd e n s i t y m =3 ( N gal =628) . . . n o r m a li s e dd e n s i t y m =4 ( N gal =281) − . . . sSFR residual )0 . . . n o r m a li s e dd e n s i t y m =5+ ( N gal =462) Figure 6.
Residual sSFRs for each of the arm number subsam-ples taken from the stellar mass-limited sample , calculated usingequations 7 and 8. The solid histograms show the distributionsfor each subsample, and the filled grey histograms indicate thesame distributions for the entire sample of star forming galaxiesfor reference. The vertical dotted lines indicate the 16th, 50th and84th percentiles.
As discussed in Sec. 2.3, the different SFR indicators thatwe use to define our total SFRs in Eq. 6 correspond to thecombination of emission from the youngest, hottest stars(measured in the UV), and emission originating from theradiation absorbed by interstellar dust and re-emitted atlonger wavelengths (the MIR). Although both sources ofemission arise from young stars of order ∼
10 Myr in age(Hao et al. 2011; Rieke et al. 2009), their relative contri-butions actually trace different phases in the molecular gasclouds from which they form. Calzetti et al. (2005) notedthat the MIR emission from galaxies traces the H α emis-sion, which itself originates from absorption of photons ofthe youngest stars ( < Myr in age), suggesting that warmdust emission is attributable to the star-forming regions ofgalaxies. UV emitting populations are instead visibly off-set from the most active star-forming regions (Calzetti et al.2005). In the absence of highly star-forming starburst galax-ies, the processes via which the UV population become ex-posed take some time, and are highly dependent on the gasand star formation conditions (Parravano et al. 2003) of themolecular clouds from which stars form.
MNRAS , 1–15 (2017) tar-formation versus arm number To give an insight into the relative fractions of ob-scured and unobscured star formation in our galaxy samples,we compare the FUV and MIR components of sSFR total inFig. 7. We use the same stellar mass-limited sample of spi-ral galaxies as used in Sec. 3.1. Each of the arm numbersubsample populations lie close to the SFMS, so we expectthem to be dominated by normal star-forming galaxies withlittle contribution from starburst populations. The amountof unobscured FUV star formation relative to the amount ofobscured MIR measured star formation is shown in Fig. 7for each of our arm number subsamples . Here, a clear trendis observed – many-armed spiral galaxies have less obscuredstar formation than the m = sample of spiral galaxies. The m = sample has the highest median log ( SFR
FUV / SFR ) value of − . ± . , corresponding to a mean of ± per cent of the SFR total being measured by the young starsunobscured by dust in the FUV. The m = , , and + values for log ( SFR
FUV / SFR ) are − . ± . , − . ± . , − . ± . and . ± . , corresponding to ± , ± , ± and ± per cent of the total star formation beingmeasured in the FUV. All of the many-armed spiral galaxysubsamples have significantly higher fractions of their totalSFR measured in the FUV than in the MIR – the KS p -values are ∼ − , ∼ − and ∼ − between the m = sample and the m = , and + samples, respectively. Themany-armed spiral samples have less obscured star forma-tion than the two-armed sample, with a greater fraction ofthe SFR measured from young stars unattenuated by dustin the FUV. β relation A common paramaterisation of the amount of dust obscura-tion in star-forming galaxies is through the IRX- β relation(Calzetti et al. 1994; Meurer et al. 1999; Calzetti et al. 2000).The quantity IRX refers to the infrared excess, and corre-sponds to the relative fraction of MIR emission originatingfrom warm dust, to the UV emission, from exposed youngstars. The quantity IRX is defined by Boquien et al. (2012)as: IRX = log ( L dust / L FUV ) . (9)The quantity β measures the slope in the UV continuum ofgalaxies, which depends on both the intrinsic UV slope, β ,and the UV slope induced by dust reddening, and is definedin Boquien et al. (2012): β = M FUV − M NUV . ( λ FUV / λ NUV ) − . (10)For starbursting galaxies, the relationship between IRXand β has been shown to be very tight, with galaxies withgreater IRX having a greater UV slope (Meurer et al. 1999;Kong et al. 2004; Overzier et al. 2011). Quiescently star-forming galaxies, however, lie below the IRX- β law for star-bursting galaxies, and show significantly more scatter. Con-tributions to both the MIR and the UV from aging stellarpopulations, variations in the dust extinction properties orvariations in star formation histories (SFHs) of star-formingregions have all been hypothesised as reasons why star-forming galaxies show this scatter (Bell 2002; Kong et al.2004; Boquien et al. 2009, 2012). . . . . n o r m a li s e dd e n s i t y m =1 ( N gal =148) . . . . n o r m a li s e dd e n s i t y m =2 ( N gal =1341) . . . . n o r m a li s e dd e n s i t y m =3 ( N gal =628) . . . . n o r m a li s e dd e n s i t y m =4 ( N gal =281) − . − . . . SFR
FUV /SFR )0 . . . . n o r m a li s e dd e n s i t y m =5+ ( N gal =462) Figure 7. sSFRs measured in the FUV and MIR for the stellarmass-limited samples . The grey filled histogram shows the samedistribution for all galaxies in the stellar mass-limited sample ,irrespective of morphology. The vertical lines show the median,16th and 84th percentiles for each of the arm number subsamples . We select galaxies from the stellar mass-limited sam-ple with
SNR > detections in the GALEX FUV, GALEXNUV, and WISE µ m , giving 7927 galaxies in total. Thesubset of galaxies classified as spirals using the criteria de-scribed in Sec. 2.2 consists of 2857 galaxies. The total dustemission, L dust , is taken from the catalogue of Chang et al.(2015), which fit stellar and dust emission curves to eachof the galaxies. The resulting IRX- β relation for our armnumber subsamples are shown in Fig. 8.All of our spiral galaxy populations lie below the IRX- β relation from Kong et al. (2004), with no significantly en-hanced starburst-like formation. In order to measure howclosely each of our samples lie to the expected IRX- β rela-tion of Boquien et al. (2012) (the dotted lines in Fig. 8), themedian offset from the relation for a given β is calculated; ifa galaxy population lies below the relation, it has a negativemedian offset, and if it lies above the line, the median offsetis positive. For reference, the full sample of galaxies irre-spective of morphology (shown by the filled grey contours inFig 8) has a median offset of − . ± . , indicating that thispopulation is representative of a normal star-forming galaxypopulation that follows the IRX- β relation of Boquien et al.(2012). The corresponding offsets for each of the arm num-ber subsamples are − . ± . , − . ± . , − . ± . , − . ± . and − . ± . . Each of the spiral galaxy popu-lations actually lie below the IRX- β relation, indicating that MNRAS000
SNR > detections in the GALEX FUV, GALEXNUV, and WISE µ m , giving 7927 galaxies in total. Thesubset of galaxies classified as spirals using the criteria de-scribed in Sec. 2.2 consists of 2857 galaxies. The total dustemission, L dust , is taken from the catalogue of Chang et al.(2015), which fit stellar and dust emission curves to eachof the galaxies. The resulting IRX- β relation for our armnumber subsamples are shown in Fig. 8.All of our spiral galaxy populations lie below the IRX- β relation from Kong et al. (2004), with no significantly en-hanced starburst-like formation. In order to measure howclosely each of our samples lie to the expected IRX- β rela-tion of Boquien et al. (2012) (the dotted lines in Fig. 8), themedian offset from the relation for a given β is calculated; ifa galaxy population lies below the relation, it has a negativemedian offset, and if it lies above the line, the median offsetis positive. For reference, the full sample of galaxies irre-spective of morphology (shown by the filled grey contours inFig 8) has a median offset of − . ± . , indicating that thispopulation is representative of a normal star-forming galaxypopulation that follows the IRX- β relation of Boquien et al.(2012). The corresponding offsets for each of the arm num-ber subsamples are − . ± . , − . ± . , − . ± . , − . ± . and − . ± . . Each of the spiral galaxy popu-lations actually lie below the IRX- β relation, indicating that MNRAS000 , 1–15 (2017)
Hart et al. − . − . − . . . β . . . . . I R X All galaxies ( N gal =7927) m =1 spirals ( N gal =147) − . − . − . . . β . . . . . I R X All galaxies ( N gal =7927) m =2 spirals ( N gal =1339) − . − . − . . . β . . . . . I R X All galaxies ( N gal =7927) m =3 spirals ( N gal =628) − . − . − . . . β . . . . . I R X All galaxies ( N gal =7927) m =4 spirals ( N gal =281) − . − . − . . . β . . . . . I R X All galaxies ( N gal =7927) m =5+ spirals ( N gal =462) Kong+04Boquien+12
Figure 8.
IRX (from Eq. 9) vs. β (from Eq. 10), for each spiral arm number. The underlying grey contours show the same distributionfor all galaxies in the stellar mass-limited sample with detections in the GALEX FUV and the WISE µ m , regardless of morphology.The solid lines show the same values for our stellar mass-limited spiral sample , split by spiral arm number. The black dashed line showsthe IRX- β relation measured for starburst galaxies (Kong et al. 2004) and the black dotted line shows the relationship for low-redshiftstar-forming galaxies (Boquien et al. 2012). they are less luminous in the MIR than expected for their β . We also see a clear trend with spiral arm number – the m = and m = populations lie much closer to the IRX- β realtion for normal star-forming galaxies, whereas galaxieswith more spiral arms lie further below the relation, indi-cating that they have more UV emission relative to MIRemission than expected for their measured β . We will dis-cuss the implications of this further in Sec. 4.1. The amount of gas that galaxies contain is usually relatedto both the current star formation activity (Huang et al.2012; Saintonge et al. 2011, 2013, 2016) and galaxy mor-phology (Helmboldt et al. 2004, 2005; Saintonge et al. 2012;Masters et al. 2012). However, the amount of gas in galaxydiscs has little dependence on the presence of spiral structureor its type, with spiral structure instead believed to rear-range the star-forming material in galaxies (Vogel et al. 1988;Elmegreen 2002; Dobbs et al. 2011; Moore et al. 2012). Byusing the atomic gas mass measurements of ALFALFA (Gio-vanelli et al. 2005; Haynes et al. 2011), we consider whetherspiral structure has any link to an excess or deficiency of gasin our spiral samples. Although stars form out of molecular hydrogen, molecular clouds form out of the diffuse mediumof atomic hydrogen (Haynes et al. 2011). This means thatalthough H i does not directly probe the amount of star-forming material available for current star formation, it doesmeasure the amount of material for potential star formation.The H i fraction, f H i = M H i / M (cid:12) exhibits a strong dependencewith stellar mass, with more massive galaxies having lowergas fractions (Haynes & Giovanelli 1984; Cortese et al. 2011;Saintonge et al. 2016). It is therefore useful to define the ex-pected gas fraction as a function of stellar mass, in order todefine whether a galaxy is deficient in H i for its stellar mass.The value for log ( M H i / M (cid:12) ) expected can be calculated in a sim-ilar way to sSFR expected in Sec. 3.1, by fitting a line to theplot of log ( M ∗ ) vs. log ( M H i / M ∗ ) . The parent sample for thiscomparison comprises of galaxies in the stellar mass-limitedsample , including all galaxies with an H i detection, regard-less of morphology. In order to probe the entire range of gasfractions, we use all galaxies from the stellar mass-limitedsample with a reliable H i detection, giving 2,434 galaxies intotal. Galaxies that fall below the H i completeness limit with M H i < . are weighted by / V max , described in Sec. 2.2.The plot of gas fraction vs. stellar mass for this sample isshown in Fig. 9. The best fit line to the data, with each point MNRAS , 1–15 (2017) tar-formation versus arm number . . . . . . M ∗ /M (cid:12) ) − . − . − . . l og ( M H I / M ∗ ) All HI detected ( N gal =2434) log( M HI /M ∗ ) = − . M ∗ ) + 6 . Figure 9.
Gas fraction as a function of stellar mass for all galaxiesin the stellar mass-limited sample with an H i detection. The filledgrey contours show where 20, 40, 60 and 80% of the galaxies lie,weighted by each galaxy’s / V max -value. The green line shows thebest fit line to the data, with each point again weighted by / V max .The dashed black line indicates the lower stellar mass limit of thedataset. m . . . . f d e t ec t e d α detected Figure 10.
Fraction of galaxies in the α i flux, in accordance with Haynes et al. (2011).The errorbars show the 1 σ error calculated in accordance withCameron (2011). weighted by / V max , yields the following relationship: log ( M H i / M ∗ ) expected = − .
70 log ( M ∗ / M (cid:12) ) + . . (11)The scatter in this relationship is . dex. One can nowmeasure the H i deficiency using (Masters et al. 2012): log ( M H i / M ∗ ) deficiency = log ( M HH i / M ∗ ) expected − log ( M H i / M ∗ ) , (12)where log ( M H i / M ∗ ) expected is given in Eq. 11. Galaxies withhigher gas fractions than expected for their stellar mass havenegative H i deficiency, and galaxies with low H i fractionshave positive H i deficiency.As in Sec. 3.1, we begin by comparing the completenessof our arm number subsamples . The fraction of the stellarmass-limited sample of ALFALFA targeted spiral galaxieswith a single detection in the α
70 catalogue as a function ofarm number is shown in Fig. 10. As was the case in for theFUV and MIR fluxes, we do see a preference for more of themany-armed galaxies to have measured H i fluxes. However, . . . . n o r m a li s e dd e n s i t y m =1 ( N gal =46) . . . . n o r m a li s e dd e n s i t y m =2 ( N gal =489) . . . . n o r m a li s e dd e n s i t y m =3 ( N gal =237) . . . . n o r m a li s e dd e n s i t y m =4 ( N gal =102) − . . . M HI /M (cid:12) ) deficiency . . . . n o r m a li s e dd e n s i t y m =5+ ( N gal =192) Figure 11. H i deficiency, calculated using equations 11 and 12,for each of the arm number subsamples . The underlying grey his-tograms show the distributions for all galaxies with detected H i ,irrespective of morphology and the solid lines show the same dis-tributions for all galaxies split by spiral arm number. Each H i detection is weighted by / V max , and the vertical lines show thepositions of the median, 16th and 84th percentiles for each spiralarm number. The dotted vertical lines show the median, 16th and84th percentiles of each of the distributions. we note that as in Sec. 3.1, the overall completeness is sim-ilar, with each of the samples having detection fractions of ∼ stellar mass-limited sample of spirals,and the distributions are plotted in Fig. 11. Only galaxieswith ALFALFA detections are included, giving 1,066 spiralgalaxies in total. To ensure that a full range of gas massesis probed, we include all α
70 detections and apply a V max weighting to the H i detections that fall below the H i com-plete mass of log ( M H i ) =9.89. The resulting H i deficiency dis-tributions are plotted in Fig. 11. Here, we see that m = galaxies are more deficient in gas than many-armed galax-ies. The median H i deficiencies are − . ± . , − . ± . , − . ± . , − . ± . and − . ± . for m = , , , and + respectively. We see a trend that many-armed spiralgalaxy samples are more H i rich than m = galaxy sam-ples. Although we cannot rule out the null hypothesis thatthe m = sample is from the same parent distribution, asthe KS p -value is 0.31, it is unlikely that this is the case forthe m = and m = + arm number subsamples with respect MNRAS000
70 detections and apply a V max weighting to the H i detections that fall below the H i com-plete mass of log ( M H i ) =9.89. The resulting H i deficiency dis-tributions are plotted in Fig. 11. Here, we see that m = galaxies are more deficient in gas than many-armed galax-ies. The median H i deficiencies are − . ± . , − . ± . , − . ± . , − . ± . and − . ± . for m = , , , and + respectively. We see a trend that many-armed spiralgalaxy samples are more H i rich than m = galaxy sam-ples. Although we cannot rule out the null hypothesis thatthe m = sample is from the same parent distribution, asthe KS p -value is 0.31, it is unlikely that this is the case forthe m = and m = + arm number subsamples with respect MNRAS000 , 1–15 (2017) Hart et al. to the m = sample, where the corresponding p -values are ∼ − and ∼ − . One of the key features via which a grand design spiral pat-tern may emerge is via a bar instability (Kormendy & Nor-man 1979). The exact nature of the dependence of granddesign spiral structure on the presence of a bar in a galaxydisc is not fully understood, since many-armed spiral galax-ies can still exist in the presence of a bar, and not all granddesign spiral galaxies host strong bars. Nonetheless, bars aremore common in grand design spiral galaxies (Elmegreen &Elmegreen 1982, 1987a). Bars can affect the gas and star for-mation properties of their host galaxies (Athanassoula 1992;Oh et al. 2012; Masters et al. 2012). In previous sections, wehave removed any galaxies with strong bars from the sam-ple by only selecting galaxies with P bar ≤ . . To assess theimpact that the presence of bars have on spiral galaxies andunderstand whether the differences in the galaxy popula-tions are driven by the presence of bars with spiral structure,the properties of barred and unbarred galaxies are now com-pared. We include all spirals in this analysis, with no cut on p bar for this section.GZ2 has collected visual classifications of spiral galax-ies, which have been used to define galaxies with and withoutbars. We use the same prescription of Masters et al. (2011)by selecting galaxies with p bar > . as barred. The fractionof galaxies with bars is significantly higher for the m = sample, with ± per cent of galaxies having bars, com-pared to – per cent for each of the many-armed samples.This confirms the results of previous studies (e.g., Elmegreen& Elmegreen 1982, 1987a) for our sample: two-armed granddesign spiral galaxies are more likely to host a bar thanmany-armed spiral galaxies. In the previous sections, the total SFRs of spiral galaxieshave been shown to differ little with respect to spiral armnumber. However, more of the star formation is obscured inthe m = population. The total gas fractions among all ofthe galaxies with a detection in α
70 also show that there isalso a weak trend for many-armed spiral galaxies to be moreH i rich. Masters et al. (2012) showed that the ALFALFA-measured H i fractions are much lower in barred galaxies,which may explain why fewer two-armed spiral galaxies havean H i detection in our sample.Each of our many-armed samples comprise of fewergalaxies than the two-armed galaxy sample, and only a smallnumber of those have bars. In order to compare the prop-erties of barred and unbarred samples of galaxies with dif-ferent arm numbers with good number statistics, we electto group our 3, 4, and 5+ armed spiral galaxies. We deemthis to be reasonable, since any trends seen in each of themany-armed spiral galaxy samples have been shown to besimilar when compared to the m = sample. In this analy-sis, we include all galaxies classified as spiral, now includinggalaxies with p bar > . , which were removed for the earlierresults. We first compare the completeness of the GALEX . . . . f d e t ec t e d SNR
FUV ≥ SNR µ m ≥ SNR
FUV , µ m ≥ > > m . . . . f d e t ec t e d α detected Figure 12.
Top panel: fraction of galaxies with GALEX FUVand WISE µ m detections for each of the barred and unbarredspiral samples. Bottom panel: fraction of the galaxies in the α ± σ errors, calculated according using the method of Cameron(2011). FUV, WISE µ m and α
70 in Fig. 12. Here we see that theoverall completeness of each of these measures decreases forstrongly barred galaxies, yet the detection fractions are stillconsistently higher for many-armed spirals.In order to check whether the presence of bars in ourgalaxy arm number samples affect the IRX- β trends inSec. 3.2.1, we subdivide the sample of spiral galaxies intofour bins of bar strength, defined using the GZ2 p bar statis-tic. The resulting IRX- β relations for the m = and the m > samples are shown in Fig. 13. The median offsets from theBoquien et al. (2012) relation are − . ± . , − . ± . , . ± . and . ± . for each of the bar strength bins fortwo-armed spirals. The corresponding offsets for the many-armed spirals are − . ± . , − . ± . , − . ± . and − . ± . . These results therefore show that with orwithout the presence of a bar, many-armed spirals are moreUV luminous than expected for normal star-forming galaxiesthan two-armed spiral galaxies.It is evident from the top row of Fig. 13 that bars af-fect both IRX and β in two-armed spirals, without causingany significant deviation from the IRX- β relation for normalstar-forming galaxies. In Sec. 3.1, we compare the total SFRs of spiral galaxieswith different arm numbers, finding only marginal differ-ences between the samples. We note that galaxies with dif-
MNRAS , 1–15 (2017) tar-formation versus arm number . . . . . m = 2 , ≤ p bar < . N gal = 962 m = 2 , . ≤ p bar < . N gal = 524 m = 2 , . ≤ p bar < . N gal = 394 m = 2 , . ≤ p bar < N gal = 648 − . − . − . . . . . . . . m > , ≤ p bar < . N gal = 1079 − . − . − . . . m > , . ≤ p bar < . N gal = 292 − . − . − . . . m > , . ≤ p bar < . N gal = 167 − . − . − . . . m > , . ≤ p bar < N gal = 184 Kong+04Boquien+12 β I R X Figure 13.
IRX- β for m = and m > many-armed spiral galaxies with and without bars. The filled grey contour shows the distributionfor all galaxies from the stellar mass-limited sample , including galaxies of all morphologies. Four bins of GZ2 p bar run from left to right for m = galaxies (top row) and m > galaxies (bottom row), and their respective points are indicated by the solid contours. The contoursindicate the regions enclosing 20, 40, 60 and 80% of the points for each sample. The measured IRX- β relations for normal star-forminggalaxies (Boquien et al. 2012) and starburst galaxies (Kong et al. 2004) are shown for reference. ferent spiral arm numbers occupy similar ranges of stellarmass (see Fig. 2) and find no enhancement in the measuredSFR of the two-armed spirals relative to the many-armedspirals. Rather, galaxies with more spiral arms have slightlyhigher detection fractions (and hence less likelihood of verylow SFR) in both the UV and MIR. For galaxies with se-cure measurements, 3- and 4-armed galaxies have marginallyhigher average sSFRs than those in the two-armed sample.Many-armed spiral patterns occur readily in simulationsof undisturbed discs, and tend to be transient in nature (Bot-tema 2003; Baba et al. 2009; Grand et al. 2012; Baba et al.2013; D’Onghia et al. 2013; Roca-F`abrega et al. 2013). Incontrast, stable two-armed spiral patterns usually requiresome form of perturbation (Sellwood 2011), in the form ofa tidal interaction, bar instability or density wave. An en-hancement in the current SFR would be expected if densitywaves were responsible for the triggering of star-formation(Roberts 1969), bars were triggering star formation in thegalaxy centre (Athanassoula 1992) or if there were ongoingtidal interactions (Barton et al. 2000; Ellison et al. 2008)in two-armed galaxies. Such mechanisms should not be evi-dent in many-armed galaxies. Our results show no strong ev-idence for any SFR enhancement in two-armed spiral galax-ies. These results therefore support those of Elmegreen &Elmegreen (1986), Stark et al. (1987) and Willett et al.(2015), where it was found that different forms of spiralstructure do not lead to a deviation from the total SFR re-lations of local galaxies. They are also consistent with Foyleet al. (2011) and Choi et al. (2015), where there was no con-clusive evidence for the triggering of star formation by granddesign spiral arms themselves. Instead, our results favour a scenario where spiral arms simply reflect the arrangementof star-forming material in galaxies, without being directlyresponsible for the triggering of star formation (Vogel et al.1988; Elmegreen 2002; Moore et al. 2012). Spiral arms are regions of both increased star formation anddust obscuration (Helou et al. 2004; Calzetti et al. 2005;Grosbøl & Dottori 2012). In Sec. 3.2 we find that, althoughoverall SFRs are seemingly unaffected by spiral arm number,the fraction of the young stars that are obscured by dustdiffers significantly.At a given star formation rate, two-armed spirals dis-play more MIR dust emission, indicating that a greater pro-portion ( ∼ per cent) of their young stellar populationresides in heavily obscured regions. This is likely due to dif-ferent relative distributions of star-formation and dust ingalaxies with different numbers of spiral arms.If we consider the IRX- β diagram, we see that (un-barred) galaxies with all numbers of arms have similar β dis-tributions, indicating that the amount of extinction affectingthe observed UV light does not vary substantially with spi-ral structure. On the other hand, IRX varies substantially,indicating more extinction for two-armed spirals. In order toavoid modifying β , this additional extinction must be in theform of heavily obscured regions, from which almost no UVescapes. Therefore, it is the relative distribution of youngstars and regions of high extinction which varies with armnumber.However, regions of very high dust extinction are the MNRAS000
IRX- β for m = and m > many-armed spiral galaxies with and without bars. The filled grey contour shows the distributionfor all galaxies from the stellar mass-limited sample , including galaxies of all morphologies. Four bins of GZ2 p bar run from left to right for m = galaxies (top row) and m > galaxies (bottom row), and their respective points are indicated by the solid contours. The contoursindicate the regions enclosing 20, 40, 60 and 80% of the points for each sample. The measured IRX- β relations for normal star-forminggalaxies (Boquien et al. 2012) and starburst galaxies (Kong et al. 2004) are shown for reference. ferent spiral arm numbers occupy similar ranges of stellarmass (see Fig. 2) and find no enhancement in the measuredSFR of the two-armed spirals relative to the many-armedspirals. Rather, galaxies with more spiral arms have slightlyhigher detection fractions (and hence less likelihood of verylow SFR) in both the UV and MIR. For galaxies with se-cure measurements, 3- and 4-armed galaxies have marginallyhigher average sSFRs than those in the two-armed sample.Many-armed spiral patterns occur readily in simulationsof undisturbed discs, and tend to be transient in nature (Bot-tema 2003; Baba et al. 2009; Grand et al. 2012; Baba et al.2013; D’Onghia et al. 2013; Roca-F`abrega et al. 2013). Incontrast, stable two-armed spiral patterns usually requiresome form of perturbation (Sellwood 2011), in the form ofa tidal interaction, bar instability or density wave. An en-hancement in the current SFR would be expected if densitywaves were responsible for the triggering of star-formation(Roberts 1969), bars were triggering star formation in thegalaxy centre (Athanassoula 1992) or if there were ongoingtidal interactions (Barton et al. 2000; Ellison et al. 2008)in two-armed galaxies. Such mechanisms should not be evi-dent in many-armed galaxies. Our results show no strong ev-idence for any SFR enhancement in two-armed spiral galax-ies. These results therefore support those of Elmegreen &Elmegreen (1986), Stark et al. (1987) and Willett et al.(2015), where it was found that different forms of spiralstructure do not lead to a deviation from the total SFR re-lations of local galaxies. They are also consistent with Foyleet al. (2011) and Choi et al. (2015), where there was no con-clusive evidence for the triggering of star formation by granddesign spiral arms themselves. Instead, our results favour a scenario where spiral arms simply reflect the arrangementof star-forming material in galaxies, without being directlyresponsible for the triggering of star formation (Vogel et al.1988; Elmegreen 2002; Moore et al. 2012). Spiral arms are regions of both increased star formation anddust obscuration (Helou et al. 2004; Calzetti et al. 2005;Grosbøl & Dottori 2012). In Sec. 3.2 we find that, althoughoverall SFRs are seemingly unaffected by spiral arm number,the fraction of the young stars that are obscured by dustdiffers significantly.At a given star formation rate, two-armed spirals dis-play more MIR dust emission, indicating that a greater pro-portion ( ∼ per cent) of their young stellar populationresides in heavily obscured regions. This is likely due to dif-ferent relative distributions of star-formation and dust ingalaxies with different numbers of spiral arms.If we consider the IRX- β diagram, we see that (un-barred) galaxies with all numbers of arms have similar β dis-tributions, indicating that the amount of extinction affectingthe observed UV light does not vary substantially with spi-ral structure. On the other hand, IRX varies substantially,indicating more extinction for two-armed spirals. In order toavoid modifying β , this additional extinction must be in theform of heavily obscured regions, from which almost no UVescapes. Therefore, it is the relative distribution of youngstars and regions of high extinction which varies with armnumber.However, regions of very high dust extinction are the MNRAS000 , 1–15 (2017) Hart et al. same places in which stars form, and so their distributionsare closely related. A number of possibilities seem to be ad-mitted by our results. Consider a single star-forming molec-ular cloud within a galaxy spiral arm. The fraction of youngstars which are heavily obscured could depend on the cover-ing fraction of surrounding, but otherwise unrelated, molec-ular clouds. Alternatively, it may depend on the degree towhich the young stars have escaped their own birth cloud. Inthe first case, the obscured fraction is determined primarilyby geometry: by the relative spatial distribution (and per-haps sizes) of star-forming regions. In the second scenario,the obscured fraction is related to the time since the re-gion commenced star-formation, and perhaps other physicalproperties of the molecular cloud.Grand design spiral arms are typically better definedand higher-contrast than many-arm structures (Elmegreenet al. 2011). We have also seen that, despite having fewerarms, they have similar total star-formation rates. These ob-servations imply that two-arm spirals have more, or larger,star formation regions in a given volume of spiral arm. Thiscould result from mechanisms associated with grand designspiral structure, such as a strong density wave, that act togather more gas and dust into spiral arm regions. For exam-ple, simulations suggest that the presence of density wavesleads to the formation of more massive molecular clouds(Dobbs et al. 2011, 2012). Since the molecular clouds presenta larger local cross section, a greater fraction of young starsare obscured by dust. The ratio of MIR to UV emission (i.e.,IRX) is therefore higher.Alternatively, the obscured fraction may be related tothe recent star-formation history. If this is more bursty innature, then more of the resulting luminosity is emitted inthe MIR than in the UV: the IRX- β relation is displacedupwards (Meurer et al. 1999; Kong et al. 2004). If star-formation in grand design spirals is driven by a triggeringmechanism – such as a tidal interaction with a compan-ion galaxy (Sundelius et al. 1987; Dobbs et al. 2010) or adensity wave (Seigar & James 2002; Kendall et al. 2015) –while many-armed spirals are not subject to the same mech-anisms, then one would expect their recent star-formationhistories to differ. Boquien et al. (2012) show that the scat-ter in IRX- β for star-forming galaxies is attributable to theintrinsic UV slope β , which is sensitive to the recent starformation history. Kong et al. 2004 suggests that for a pe-riod of ∼ Gyr following a starburst, galaxies will occupya lower position in the IRX- β plane: as the new stars es-cape their molecular birth clouds the galaxy becomes UVbright, and the declining MIR emission is not replaced byfurther star formation. As many-armed spirals lie lower inthe IRX- β plane, it is possible they are associated with a(mild) post-starburst state. In Hart et al. (2016), we showedthat a recent, rapid decline in SFR was required to producethe observed optical colours for many-armed spirals, whichwould be consistent with these observations.A further possibility is that the dispersal time of molec-ular clouds varies with spiral arm number. Although bothUV and MIR emission are associated with recent star for-mation (e.g., Hao et al. 2011; Kennicutt & Evans 2012),they actually probe different timescales in the evolution ofstar-forming regions. In nearby galaxies, UV emission is dis-placed from the H α emission that traces the most recent starformation, whereas MIR emission arises from regions much closer to the brightest H α knots (Helou et al. 2004; Calzettiet al. 2005; Crocker et al. 2015). To observe UV emission,the parental molecular cloud must be dispersed, a processthat takes ∼ Myr in local spirals (Grosbøl & Dottori 2012).However, more massive molecular clouds may take longer todisperse. The dispersion of molecular clouds may thus bea more rapid process in many-armed galaxies, with weakerspiral structure, meaning that the UV emitting populationemerges more quickly.The radial geometry of the star formation in spiralgalaxies may also be affected by the presence of differingforms of spiral structure. Since the level of dust obscura-tion is greater towards the centre of galaxies (e.g., Boissieret al. 2004; Roussel et al. 2005; Boissier et al. 2007) these re-sults could imply that star-formation occurs more centrallyin two-armed spiral galaxies, which is proposed to be thecase for barred spirals (e.g., Athanassoula 1992; Oh et al.2012). Given that bars are also associated with two-armedspiral structure (Kormendy & Norman 1979), this may havea strong influence on the observed properties of galaxies.However, in Sec. 3.4.2 we investigated what effect the pres-ence of a strong bar has on the IRX- β diagram, and foundthat the presence of bars in our galaxies led to no differencesin the offset from the IRX- β relation. This suggests that thespiral structure itself is responsible for the observed offsetsfrom the normal IRX- β relation, rather than bars and theradial geometry of star formation.Discerning between the possibilities outlined above willrequire a more careful consideration of the distribution,properties and evolution of molecular clouds within individ-ual galaxies. However, with further synthesis of empiricalresults and sophisticated modelling, further progress in un-derstanding how spiral arms relate to star-formation seemspromising. Gas plays a critical role in sustaining spiral structure indiscs. Gas in discs contributes to the growth of spiral per-turbations via swing amplification in both grand design andmany-armed spirals (Jog 1992, 1993). The accretion of coolgas onto galaxy discs can also help sustain many-armed pat-terns. The role that the amount of gas plays in galaxieswith different spiral arm numbers was considered in Sec. 3.3.Given that gas could potentially amplify or sustain bothtwo-armed (Ghosh & Jog 2015, 2016) and many-armed spi-ral structure (Jog 1993), then it is expected that all of ourgalaxy samples should contain significant quantities of H i .We found that many-armed spiral galaxies are the most gasrich, whereas two-armed spirals are the most gas deficient.Given that the total SFRs are similar for all of our samples,this implies that H i is converted to stars more efficiently intwo-armed spirals than in many-armed spirals. As swing am-plification acts to amplify all types of spiral structure, it isunclear why different spiral arm patterns would be more orless gas rich. It is perhaps the case that a higher gas fractionis required to sustain a many-armed spiral pattern in galaxydiscs.Another factor to be considered is the presence of barsin our spiral galaxies. In our analysis, we remove all stronglybarred galaxies, yet still see a trend for two-armed galax-ies, which are usually associated with bar instabilities, to be MNRAS , 1–15 (2017) tar-formation versus arm number the most gas poor (Davoust & Contini 2004; Masters et al.2012). Therefore, variation in the gas fraction must also re-late directly to differences in spiral arm structure or to thepresence of weak bars. In this paper, the star formation properties of spiral galax-ies were investigated with respect to spiral arm number. Asample of galaxies was selected from SDSS, using the visualclassification statistics of Galaxy Zoo 2 (GZ2). Using pho-tometry from GALEX, SDSS and WISE, total star forma-tion rates were compared by combining measures of unob-scured star-formation from UV emission and obscured star-formation from the MIR. Many-armed spiral galaxies areless likely to have very low sSFRs and thus be undetectedin the UV or MIR. However, for galaxies with reliable UVand MIR detections, sSFR has no significant dependence onspiral arm number. Despite this, we find that spirals with dif-ferent numbers of arms do have different levels of dust obscu-ration, with many-armed spirals having more UV emissionfrom young stars unobscured by dust. This is most evidentwhen comparing the IRX- β relation, where IRX measuresthe relative fraction of MIR to UV emission, and β is theUV slope. Many-armed spirals have significantly lower IRXfor a given β . We have discussed several possibilities thatcould give rise to our findings, individually or in combina-tion:(i) The differences could be due to the relative distribu-tion of star forming regions in galaxies with different spiralstructure. In grand design spirals, the molecular clouds maybe more concentrated in the dense arm regions. The conse-quent increase in dust obscuration may lead to a reductionin UV emission compared to that in the MIR.(ii) More generally, molecular cloud properties, e.g. massand size distributions, may differ in discs hosting two or morespiral arms. In this case, in addition to geometrical effects,molecular clouds may take longer to disperse in two-armedgalaxies. The UV emitting population would thus emergeover a longer timescale, leading to an enhanced IRX.(iii) Our results also appear consistent with many-armedspirals having recently experienced a rapid decline in star-formation rate.Two-armed spirals are more gas deficient than many-armed spirals, meaning they are more efficient at convertingto stars. Two-armed spirals are also more likely to host bars,with ∼ per cent having strong bars compared to only ∼ per cent of many-armed galaxies. However, we show thatbars only serve to move galaxies along the normal IRX- β relation: strongly barred galaxies have higher levels of MIRemission as well as steeper UV slopes. Spiral arm number,on the other hand, has a significant effect on how far spiralsare offset perpendicular to the normal IRX- β relation. ACKNOWLEDGEMENTS
The data in this paper are the result of the efforts of theGalaxy Zoo 2 volunteers, without whom none of this work would be possible. Their efforts are individually acknowl-edged at http://authors.galaxyzoo.org .The development of Galaxy Zoo was supported in partby the Alfred P. Sloan foundation and the Leverhulme Trust.RH acknowledges a studentship from the Science andTechnology Funding Council, and support from a Royal As-tronomical Society grant.Plotting methods made use of scikit-learn (Pe-dregosa et al. 2011) and astroML (Vanderplas et al. 2012).This publication also made extensive use of the scipy
Python module (Jones et al. 01 ), and
TOPCAT (Taylor 2005)and
Astropy
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