The evolution of the radial gradient of Oxygen abundance in spiral galaxies
M.Mollá, A.I.Díaz, Y.Ascasibar, B.K.Gibson, O.Cavichia, R.D.D.Costa, W.J.Maciel
aa r X i v : . [ a s t r o - ph . GA ] D ec Chemical Abundances in Gaseous NebulaeAAA Workshop Series 12, 2016G. Hägele, M. Cardaci & E. Pérez-Montero, eds.
Invited Review
The evolution of the radial gradient of Oxygen abundancein spiral galaxies
M. Mollá , A.I. Díaz , , Y. Ascasibar , , B.K. Gibson , O. Cavichia ,R.D.D. Costa , and W.J. Maciel CIEMAT, Avda. Complutense 40, 28040 Madrid, Spain Universidad Autónoma de Madrid, 28049, Madrid, Spain Astro-UAM, Unidad Asociada CSIC, Universidad Autónoma deMadrid,28049, Madrid, Spain E.A Milne Centre for Astrophysics,University of Hull, HU6 7RX, United Kingdom Instituto de Física e Química, Universidade Federal de Itajubá, Av.BPS, 1303, 37500-903, Itajubá-MG, Brazil Instituto de Astronomia, Geofisica e Ciências Atmosféricas,Universidade de Sâo Paulo, 05508-900, Sâo Paulo-SP, Brazil
Abstract.
The aim of this work is to present our new series of chemicalevolution models computed for spiral and low mass galaxies of differenttotal masses and star formation efficiencies. We analyze the results ofmodels, in particular the evolution of the radial gradient of oxygen abun-dance. Furthermore, we study the role of the infall rate and of the starformation history on the variations of this radial gradient. The relationsbetween the O/H radial gradient and other spiral galaxies characteristicsas the size or the stellar mass are also shown. We find that the radialgradient is mainly a scale effect which basically does not change with theredshift (or time) if it is measured within the optical radius. Moreover,when it is measured as a function of a normalized radius, show a simi-lar value for all galaxies masses, showing a correlation with a dispersionaround an average value which is due to the differences star formation ef-ficiencies, in agreement with the idea of a universal O/H radial gradient.
1. Introduction
The elemental abundances in spiral and low mass galaxies are lower in the outerregions than in the inner ones, showing a well characterized radial gradient de-fined by the slope of a least-squares straight line fitted to the radial distributionof these abundances along the galactocentric radius (Shaver et al. 1983; Zaristkyet al, 1994; Henry & Worthey 1999). These radial gradients seem to correlatewith other characteristics defining their galaxies. This way, they are flatter inthe early galaxies than in the late ones. They also seem steeper in the low massgalaxies than in the bright massive disks. This radial gradient is considered asan evolutionary effect, that is, it comes from a difference of enrichment betweenregions more evolved (at the inner parts of disk) compared with the less evolveszones of the outer disks. This way, a flat gradient implies a more rapid evolution1
Mollá et al. than in disks where the gradient is steeper, as shown in Mollá, Ferrini & Díaz(1996) for a set of models for some nearby galaxies. These models resulted in asteep radial gradient for NGC 300 or M 33, while M 31 had a flatter gradientthan our Milky Way Galaxy (MWG), and other similar galaxies as NGC 628 orNGC 6946. Since the evolution modifies the level of enrichment of a given regionor galaxy, it is expected that the radial gradient also changes with time and,therefore, that high-intermediate redshift galaxies would have to show a steeperradial gradient than in the present time, at least when measured as dex kpc − .This results was obtained in Mollá, Ferrini & Díaz (1997), further obtained laterin Mollá & Díaz (2005), hereafter MD05, and was also supported by the Plane-tary Nebulae (PN) O/H abundance data (Maciel, Costa & Uchida 2003) and byopen stellar cluster metallicities for different ages bins. Results by cosmologicalsimulations for a MWG-like galaxy also obtained a similar behavior (Pilkingtonet al. 2012).However, when a correct feedback is included in these simulations, the radialgradient results to have a very similar slope for all times/redshifts (Gibson et al.2013). In turn, the most recent PN data (Stanghellini & Haywood 2010, Maciel& Costa 2013, Magrini et al. 2016) refined to estimate with more precision theirages and distances, give now the same result: there is no evidences of evolution ofthe radial gradient with time for MWG nor for other close spiral galaxies, at leastuntil z = 1 . . Simultaneously, there are, however, some recent observational datawhich estimate the abundances of galaxies at high and intermediate redshift, andwhich obtain a plethora of different radial gradients with values as different as-0.30 dex kpc − or +0 . dex kpc − (Cresci et al. 2010, Yuan et al. 2011, Queyrelet al. 2012, Jones et al. 2013, Genovali et al. 2014, Jones et al. 2015, Xiang etal. 2015, Anders et al. 2016). It is therefore necessary to revise our chemicalevolution models and analyze in detail the evolution of this radial gradient notonly for the MWG, but also for different galaxies.
2. Chemical evolution model description
We have computed a series of 76 models applied to spiral galaxies with dynamicalmasses in the range × – M ⊙ (with mass step in logarithmic scale of ∆ log M = 0 . ) which implies disk total masses in the range . × – . × M ⊙ , or, equivalently rotation velocities between 42 and 320 km s − . Theradial distributions of these masses are calculated through equations from Salucciet al.(2007), based in the rotation curves and their decomposition in halo anddisk components.The scenario is the same as the one from MD05, with the total mass in a sphericalregions at the time t = 0 , which infall over the equatorial plane and forms out thedisk. The gas infall rates are computed by taking into account the relationshipbetween halo mass and disk mass in order to obtain at the end of the evolutiondisks as observed, with the adequate mass. They result to be higher in thecenters of disks (bulges) and lower in disks, decreasing towards the outer regions,as expected in an inside-out scenario. However, the evolution with redshift isvery similar for all disk regions, only with differences in the absolute valuesof infall rates, but with a smooth decreasing for decreasing z , except for thecentral regions for which the infall changes strongly with z , more similarly to the he evolution of Oxygen radial gradient n = 1 . .In the disk, however, we have a star formation law in two steps: first molecularclouds form from diffuse gas, then stars form from cloud-cloud collisions (or bythe interaction of massive stars with the molecular clouds surrounding them).In our classical standard models from MD05, we treated these processes as de-pending on the volume of each region and a probability factor or efficiency foreach one. For the halo SF, it is assumed an efficiency constant for all galaxies.The process of interaction of massive stars with clouds is considered as local andwe use the same approach for all galaxies. The two other efficiencies definingthe molecular clouds and stars formation processes are modified simultaneouslyfrom a model to another, with values between 0 and 1.In this new series of models we have also used an efficiency to form stars frommolecular clouds, but to convert diffuse gas into molecular phase we have triedsix different methods, two based in the same efficiency method as in MD05,called STD and MOD, and four based in different prescriptions based in Blitz& Rosolowsky (2006), Krumhold et al (2008, 2009), Gnedin & Kravtsov (2011),and Ascasibar et al. (in preparation), so-called BLI, KRU, GNE, and ASC,respectively. More details about these calculations and their implementation inour code are given in Mollá et al. (submitted), where we have applied the modelsto MWG and have checked which of these techniques give the best results whencomparing the observational data. Our results indicate that the technique ASCshows a behavior in better agreement with data than the others, In particularthose related with the ratio HI/H along radius or as a function of the gasdensity.The stellar yields are selected as derived in Mollá et al. (2015) among 144different combinations with which we calculate a MWG model to see which ofthem is the best in reproducing the MWG data. We chose the Gavilán et al(2005,2006) stellar yields for low and intermediate stars, the ones from Limongi& Chieffi (2003) and Chieffi & Limongi (2004) for massive stars, and the Kroupa(2002) IMF. The Supernova type Ia yields from Iwamoto et al (1995) are alsoused.
3. Results3.1. Evolution of the O/H radial gradient in MWG
In Fig. 1 we represent the O/H radial gradient as a function of redshift for the sixmodels for MWG calculated in Mollá et al. (2017) with the different prescriptionsof the HI to H conversion as explained. In top panels we show these gradientsas dex kpc − , computed in panel a) with the whole radial range for which wehave calculated the models. In panel b) we have the gradients calculated withregions for which R ≤ . R eff . We may see that in this last case the gradientis basically constant along z with very small differences among models. In bothpanels we have included the MWG data which give this evolution along z , PNfrom Stanghellini & Haywood (2010) and Maciel & Costa (2013); open clustersfrom Cunha et al. (2016); and stellar abundance from Anders et al. (2016). The Mollá et al.
Figure 1. Evolution of the O/H radial gradient with redshift z forthe MWG, measured as: top panels) dex kpc − and bottom panels) asdex R − . Solid lines represent our different models as labelled in c).Left panels show gradients for the whole radial range. Right panelsshow gradients only using regions within R ≤ . eff . Data are fromStanghellini & Haywood (2010, S10), Maciel & Costa (2013, M13),Cunha et al. (2016, C16), Anders et al. (2016, A16), Henry et al.(2010, H10), Rupke et al. (2010, R10), Genovali et al. (2014, G14),Sánchez et al.(2014, S14) and Mollá et al. (2015, M15), as labelled inb) and d). Cosmological simulations result for a MWG-like object fromGibson et al. (2013) is also drawn in a) and b).present time values are from Henry et al. (2010), Rupke et al. (2010), Genovaliet al. (2014) and the one compiled by Mollá et al. (2015), as labelled. We havealso shown the cosmological simulation result for a Milly Way-like galaxy fromGibson et al. (2013, G13). We see that, in order to reproduce the data, it isnecessary to compute the gradient within the optical radius. In bottom panelswe show the gradients obtained using a normalized radius ( R/R eff ). In panel c),where we use again all radial range, we see a different behavior between STDand MOD models (which use an efficiency to form molecular clouds) and allthe others using a prescription to convert HI in H which depend on the gas,stars or total density or/and on the dust through the metallicity. In these lastcases the effective radius increases more slowly than in our standard models,thus producing a strong radial gradient when regions out of the optical disk areincluded for the fit. In panel d) , where only regions with R ≤ . R eff are used, he evolution of Oxygen radial gradient eff with redshift z . Dataare from Trujillo et al (2007), Buitrago et al. (2008), and Margolet-Bentatol et al. (2016), as blue triangles, red squares, and black dots,respectively.we find again a very constant radial gradient along the redshift. In fact, thisvalue is in very good agreement with the one found by Sánchez et al. (2014,S14) as a common gradient for all the CALIFA survey galaxies.The grow of the disk in the different models is shown in Fig. 2 with data aslabelled. We see, as said before, that ASC model is the one where the radiusincreases more slowly while the STD and MOD models started very early to showa large disk. GNE, BLI and KRU show an intermediate behavior. Although thedata we show in Fig. 2 refer mainly to bulges and disks from early-type galaxies,it seems clear that ASC is the model closest to the observations. In Fig. 3 we show the radial gradients computed for different galaxy masses,as labelled, in a similar way than Fig. 1. In panel a), as in Fig.1a, the radialgradient computed for all radial regions is shown. It is clear that each galaxyhas its own evolution being the smallest one which shows the most differentbehavior. Each galaxy has a different radial gradient, with the most massiveones showing the flattest distributions ( ∼ − .
05 dex kpc − for all z ), while thesmallest has the steepest gradient ( ∼ − .
20 dex kpc − ). However, when onlyradial regions within the optical radius are used to compute the radial gradient Mollá et al.
Figure 3. Evolution of the O/H radial gradient with redshift z forseveral galaxy models with different virial masses ( M vir ), measured as:dex kpc − (top panels) and dex R − (bottom panels). Left panels showthe gradients obtained using the whole radial range available in thesimulations. Right panels show gradients computed only using regionswithin the optical disk defined as R ≤ . eff . Data correspond to theobservations by Cresci et al. (2010, yellow stars), Yuan et al. (2011,purple square), Queyrel et al. (2012 grey open dots), Jones et al. 2013(orange crosses), and Magrini et al. (2016, red points with error bars).a very different behavior arises: all gradients are approximately constant with z for galaxies with log( M vir ) ≥ . , although with the same behavior thanbefore: the more massive the galaxy, the flatter the gradient. In the lowestmasses galaxies, it is evident the moment in which the disk begins to grow: at z = 2 . for log M vir = 11 . and at z = 0 . for log M vir = 11 . .When we represent the gradients measured as function of the effective radius,we see that they steepen with decreasing z when all radial regions are used (Fig.3c) and, again, a very smooth evolution along z for all galaxies appears whenonly the optical disk is used to fit the gradient (panel d). The average valuein this case is ∼ − .
13 dex kpc − , as the value found by Sánchez et al. (2014),supporting their claim that a universal radial gradient appears for all galaxies.A common radial gradient is easily obtained drawing O/H for the present timeas a function of R/R eff for all galaxy masses and efficiencies (larger than 0.002)in a same plot, as we show in Fig.4. We see that effectively, such as Sánchezet al. (2014) found, a same radial gradient is obtained for all models, when he evolution of Oxygen radial gradient ǫ ∗ ≥ . , as a function of the normalizedradius R/R eff . Each color shows a different efficiency ǫ ∗ .R/R eff ≤ . , with a dispersion given by the differences in the star formationefficiencies around an average radial distribution.Since it seems quite evident that the radial gradient is a scale effect due tothe star formation rate which is measuring the stellar disk growth, we wouldexpect a correlation between this O/H radial gradient measured as dex kpc andthe scale length of the disk or any other quantity defining the size of the disk.We plot in Fig. 5, right panel, this correlation for all our models with differentgalaxy masses and with six different values for the efficiencies to form stars frommolecular clouds, which are coded with different colored dots. The correlation isclear for all effective radii larger than 1.25 kpc. If the effective radius is smallerthan this value, our code, working with radial regions of 1 kpc wide, is not ableto calculate a radial gradient nor an effective radius. This theoretical correlationsupports the observational one found by Bresolin & Kennicutt (2015) with theradial gradient and the scale length of the disks (their Fig. 3). These authorsclaim in that work that all galaxies, even the low surface brightness galaxies,share a common abundance radial gradient when this one is expressed in termsof the exponential disk scale-length (or any other normalization quantity).
4. Conclusions
The conclusions can be summarized as: • A grid of chemical evolution models with 76 different total dynamicalmasses in the range 10 to 10 M ⊙ is calculated. Mollá et al.
Figure 5. The O/H radial gradient measured as dex kpc − , as a func-tion of the inverse of the effective radius, 1/R eff . Each color shows adifferent efficiency ǫ ∗ . •
10 values of efficiencies ǫ ∗ to form stars from molecular clouds are usedwith values < ǫ ∗ < . But we find that useful values are only the firstsix-seven of them with ǫ ∗ > . . • The best combination IMF from Kroupa et al (2002) + Gavilan et al.(2006) + Chiefi & Limongi (2003,2004) yields, is used. The stellar yields + IMF may modify the absolute abundances on a disk, but they do notchange the radial slope of the abundance distributions of disks. • Using Shankar et al. (2006) prescriptions for M halo /M disk , we obtain thenecessary infall rates to reproduce the radial profiles of galaxy disks • Different prescriptions for the conversion of HI to H are used finding thatthe ASC model is the best one. • The slope of the oxygen abundance radial gradient for a MWG-like modelwhen it is measured for
R < . R eff has a value − . dex kpc − , whichis around − . dex R − when it is measured using a normalized radius. • This same slope is also obtained for all efficiencies and all galaxy massesin excellent agreement with CALIFA results, supporting the idea of a uni-versal radial gradient for all galaxies when measured as a function of anormalized radius. • The slope do not changes very much along z when the infall rate is assmooth as we have obtained recently, compared with old models with astronger evolution. he evolution of Oxygen radial gradient Acknowledgments.
This work has been supported by DGICYT grant AYA2013-47742-C4-4-P. This work has been sup- ported financially by grant 2012/22236-3from the São Paulo Research Foundation (FAPESP). This work has made useof the computing facilities of the Laboratory of Astroinformatics (IAG/USP,NAT/Unicsul), whose purchase was made possible by the Brazilian agency FAPESP(grant 2009/54006- 4) and the INCT-A. MM thanks the kind hospitality andwonderful welcome of the Jeremiah Horrocks Institute at the University of Cen-tral Lancashire, the E.A. Milne Centre for Astrophysics at the University of Hull,and the Instituto de Astronomia, Geofísica e Ciências Atmosféricas in São Paulo(Brazil), where this work was partially done.
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