How non-linear scaling relations unify dwarf and giant elliptical galaxies
aa r X i v : . [ a s t r o - ph . C O ] S e p How non-linear scaling relations unify dwarf and giant elliptical galaxies
Alister W. Graham , a Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia.
Abstract.
Dwarf elliptical galaxies are frequently excluded from bright galaxy samples because they do notfollow the same linear relations in diagrams involving e ff ective half light radii R e or mean e ff ective surfacebrightnesses h µ i e . However, using two linear relations which unite dwarf and bright elliptical galaxies we explainhow these lead to curved relations when one introduces either the half light radius or the associated surfacebrightness. In particular, the curved h µ i e - R e relation is derived here. This and other previously misunderstoodcurved relations, once heralded as evidence for a discontinuity between faint and bright elliptical galaxies at M B ≈ −
18 mag, actually support the unification of such galaxies as a single population whose structure (i.e.stellar concentration) varies continuously with stellar luminosity and mass.
Elliptical galaxies, and the bulges of disc galaxies, donot have structural homology (e.g. Davies et al. 1988; Caonet al. 1993; D’Onofrio et al. 1994; Young & Currie 1994,1995;Andredakis et al. 1995). Instead, they have a continuousrange of stellar concentrations — quantified by the S´ersic(1968) index n (see Figure 1a) — that varies linearly withboth stellar luminosity and central surface brightness (af-ter correcting for central stellar deficits or excess light). Anunappreciated consequence of these two linear relationswhich unite faint and bright elliptical galaxies across thealleged divide at M B ≈ −
18 mag is that relations involvingeither their e ff ective half-light radius ( R e ) or their e ff ec-tive surface brightness ( µ e ), or the mean surface brightnesswithin R e ( h µ i e ), will be non-linear. Such curved relationshave often been heralded as evidence that di ff erent physi-cal processes must be operating on faint and bright ellipti-cal galaxies because these relations have a di ff erent slopeat either end. To further complicate matters, sample selec-tion which includes faint and bright elliptical galaxies, butexcludes the intermediate luminosity population, can ef-fectively break such continuously curved relations into twoapparently disconnected relations.Figure 2 shows three diagrams for elliptical galaxies,two with linear relations that naturally explain the thirdpanel’s curved relation. The data have been taken from thecompilation by Graham & Guzm´an (2003), while the twolinear relations from that paper have been slightly tweakedhere. From the first relation between central surface bright-ness µ and S´ersic index n , given by µ = − . n ) (1)and shown in Figure 2b, one can convert µ into h µ i e usingthe S´ersic formula h µ i e = µ + . b / ln(10) − . n e b Γ (2 n ) / b n ) , (2) a e-mail: [email protected] where b ≈ . n − . ff ective radius R e is acquired by match-ing the second relation between absolute magnitude M andcentral surface brightness, given by M = . µ − . M = h µ i e − . π R , kpc ) − .
57 (4)(e.g. Graham & Driver 2005, their equation 12). Doing thisyields the expressionlog R e = ( . h µ i e + . " b ln(10) − log ne b Γ (2 n ) b n ! − . , (5)in which one knows the value of n associated with eachvalue of h µ i e from the expressions above. Equation 5, ob-tained from two empirical linear relations (equations 1 and3), is a curved relation that is shown in Figure 2c.The implications of this should not be glossed over.Without any understanding of the h µ i e - R e diagram (Fig-ure 2c), it has in the past been used to claim that faint andbright elliptical galaxies must have obtained their struc-ture from di ff erent physical processes — because the faintand bright arms of the galaxy distribution are nearly per-pendicular to each other. If there was instead one linearrelation in this diagram, it would have been claimed that asingle unifying mechanism was operating. As seen in Fig-ures 2a and 2b, linear relations do however exist across thefaint and bright end of the galaxy distribution in M - µ and n - µ space. In passing we note that because of the linearrelation between M ( = log L ) and log n (e.g. Caon et al.1993; Young & Currie 1995; Jerjen & Binggeli 1997; Gra-ham, Trujillo & Caon 2001; Ferrarese et al. 2006), and theassociated non-linear behaviour between µ and µ e (Fig-ure 1b), the relation between M and µ e is not linear. Sim-ilarly, as detailed above, the relation between h µ i e and R e PJ Web of Conferences
Fig. 1.
Panel a) S´ersic R / n surface brightness profiles with e ff ective surface brightness µ e =
10, and n =
1, 2, 3, 4, 6 and 10. Panels b) andc) show the di ff erence between the central surface brightness at R =
0, denoted by µ , and the e ff ective surface brightness µ e and themean e ff ective surface brightness h µ i e within the e ff ective radius R e . is not linear but curved. This result, however, has just beenpredicted / explained from linear relations which unify faintand bright elliptical galaxies.For those curious about the discrepant “core galaxies”in Figure 2a, this paragraph and the following one providesomething of an explanatory detour. The departure fromthe B -band M B - µ , B diagram by elliptical galaxies brighterthan M B ≈ − . > . × M ⊙ ), seen inFigure 2a, was explained by Graham & Guzm´an (2003)in terms of partially depleted cores relative to their outerS´ersic profile (see also Graham 2004; Trujillo et al. 2004;Merritt & Milosavljevi´c 2005). Such cores are thought tohave formed from dry galaxy merger events (Begelman,Blandford, & Rees 1980; Ebisuzaki, Makino, & Okumura1991) and resulted in Graham et al. (2003) and Trujillo etal. (2004) advocating a “new elliptical galaxy paradigm”based on the presence of this central stellar deficit ver-sus either none or an excess of light (see also Gavazziet al. 2005; Ferrarese et al. 2006; Cˆot´e et al. 2007; andlater Kormendy et al. 2009). As discussed in Graham &Guzm´an (2003), this distinction at M B ≈ − . M B ≈ −
18 mag (e.g. Kormendy 1985).Further evidence for this division at M B ≈ − . M B ≈ −
18 mag (Kormendy1985; Kormendy et al. 2009; Tolstoy et al. 2009), magcomes from the tendency for the brighter elliptical galaxiesto be anisotropically pressure supported systems with boxyisophotes, while the less luminous early-type galaxies arereported to have discy isophotes and often contain a rotat-ing disc (e.g. Carter 1978, 1987; Bender 1988; Peletier etal. 1990; Emsellem et al. 2007; Krajnovi´c et al. 2008). Ad-ditional support for the above mentioned dry merging sce-nario at the high-mass end is the flattening of the colour-magnitude relation above 0.5-1 × M ⊙ . As discussed byGraham (2008, his section 6) and reiterated by Bernardi et al. (2010), this flattening was evident in Baldry et al.(2004, their Figure 9) and Ferrarese et al. (2006, their Fig-ure 123), and even Metcalfe, Godwin & Peach (1994). Thisflattening has since been shown in other data sets (e.g.,Skelton, Bell & Somerville 2009, although they reportedthe transition at M R = −
21 mag, i.e. ≈ M B ≈ − . L - σ relation would be steeper atthe high-luminosity end if total, luminosity-weighted, infi-nite aperture velocity dispersions (equal to one-third of thevirial velocity dispersion) were used instead of central ve-locity dispersions, as required in equation 1 from Wolf etal. (2010) and advocated by many papers in 1997 for use inthe “Fundamental Plane” (FP: Djorgovski & Davis 1987).Returning to Figure 2, due to the linear relations in Fig-ure 2a and 2b which connect dwarf and ordinary ellipti-cal galaxies across the alleged divide at M B ≈ −
18 mag,coupled with the smoothly varying change in light profileshape as a function of galaxy magnitude, the h µ i e - R e re-lation is curved. The apparent deviant nature of the dwarfelliptical galaxies from the approximately linear section ofthe bright-end of the h µ i e - R e distribution, known as the Ko-rmendy (1977) relation, does not imply that two di ff erentphysical processes are operating.Similarly, the location of disc galaxy bulges at the faintend of this distribution does not imply that they must be“pseudobulges”. That is, “pseudobulges”, as opposed to“classical bulges”, can not be identified simply becausethey are outliers from the Kormendy (1977) relation (Gadotti2009) — the bright arm of a longer, continuous and unify-ing curved relation. While such apparent outliers are asso-ciated with bulges having low luminosities, low S´ersic in-dices, and faint central surface brightnesses, this is not byitself evidence that they experienced a di ff erent formationprocess. For similar reasons, galaxies which do not follow Universe of dwarf galaxies: Observations, Theories, Simulations Fig. 2.
Due to the observed linear relation of the B-band central surface brightness µ , B with a) the absolute magnitude M B (Eq. 3) andb) the logarithm of the S´ersic exponent n (Eq. 1), the relation between the e ff ective radius R e and the mean surface brightness withinthis radius h µ i e (Eq. 5) is highly curved for elliptical galaxies. The somewhat orthogonal distribution in panel c) is not evidence for twodi ff erent physical processes operating at the faint and bright end of the elliptical galaxy sequence. Instead it is a consequence of thetwo linear relations which unify the faint and bright end, and bridge the alleged divide between dwarf and normal elliptical galaxiesat M B ≈ −
18 mag. The “core galaxies” (large filled circles) with partially depleted cores can be seen to have lower central surfacebrightnesses than the relation in panel a). However, the inward extrapolation of their outer profile yields µ values which follow the linearrelation, as first noted by Jerjen & Binggeli (1997). The data are from the compilation by Graham & Guzm´an (2003, their figure 9).Dots represent dwarf elliptical (dE) galaxies from Binggeli & Jerjen (1998), triangles represent dE galaxies from Stiavelli et al. (2001),large stars represent Graham & Guzm´an’s (2003) Coma dE galaxies, asterix represent intermediate to bright E galaxies from Caon et al.(1993) and D’Onofrio et al. (1994), open circles represent the so-called “power-law” E galaxies from Faber et al. (1997), and the filledcircles represent the “core” E galaxies from these same authors. The S0 galaxies are excluded, pending bulge / disc decompositions. the bright arm of the curved L - R e relation (derived / explainedin Graham & Worley 2008, their figure 11) need not bepseudobulges, nor are galaxies which do not follow thebright arm of the curved Mass- R e relation (presented byGraham et al. 2006, their figure 1b). Galaxies which donot follow the bright arm of the continuous, but curved, L - h µ i e and L - µ e relation (e.g., Graham & Guzm´an 2003,their Figure 12) also need not necessarily be pseudobulges(Greene, Ho & Barth 2008; Fisher & Drory 2010).While luminous bulges and elliptical galaxies followthe same Fundamental Plane (Falc´on-Barroso, Peletier &Balcells 2002), fainter elliptical galaxies and bulges smoothlydepart from the FP (when sample selection biases do notchop out a gulf between the faint and bright systems). Thesesystems appear to follow a continuous trend along what isa curved manifold, of which the FP is the flat portion ofthis curved hypersurface (Graham & Guzm´an 2004; Gra-ham 2005; La Barbera et al. 2005; Zaritsky, Gonzalez &Zabludo ff ff from the faint end of the Fundamental need not haveformed from di ff erent physical mechanisms.In summary, using curved relations, that can be con-structed from unifying linear relations, as a means to iden-tify an allegedly di ff erent class of galaxy (i.e. dwarf el-liptical galaxies or pseudobulges) is not appropriate. Thecurved relations involving either R e or h µ i e , and also µ e (see Figure 1), do not signal a di ff erent formation mecha-nism for low- and high-luminosity elliptical galaxies. In-stead, these curved relations can be understood in terms of, and indeed predicted from, linear relations known tounify faint and bright elliptical galaxies. Understandingthe implications of structural non-homology (i.e. the rangeof stellar concentrations) among elliptical galaxies (andbulges in disc galaxies) is key to better understanding galax-ies and the connections they share. For those who attended this talk, they will know that while theabove material was presented, it was not the original nor primarysubject matter. For readers interested in the coexistence of nuclearstar clusters (NC) and massive black holes (BH), and the natureof the smooth transition from NC-dominance to BH-dominanceas the host bulge or elliptical galaxy mass increases, I refer oneto Graham & Spitler (2009) and Graham et al. (2010).
References
1. Andredakis Y.C., Peletier R.F., Balcells M., MNRAS ,(1995) 8742. Baldry I.K., Glazebrook K., Brinkmann J., Ivezi´c ˇZ., LuptonR.H., Nichol R.C., Szalay A.S., ApJ , (2004) 6813. Begelman M.C., Blandford R.D., Rees M.J., Nature ,(1980) 3074. Bender R., A&A , (1988) L75. Bernardi M., Roche N., Shankar F., Sheth R.K., MNRAS, sub-mitted (2010, arXiv:1005.3770)6. Binggeli B., Jerjen H., A&A , (1998) 177. Caon N., Capaccioli M., D’Onofrio M., MNRAS , (1993)10138. Capaccioli M.,
The World of Galaxies , ed. H. G. Corwin, L.Bottinelli (Berlin: Springer-Verlag 1989) 2089. Carter D., MNRAS , (1978) 79710. Carter D., ApJ , (1987) 514
PJ Web of Conferences
11. Cˆot´e P., et al., ApJ , (2007) 145612. Davies J.I., Phillipps S., Cawson M.G.M., Disney M.J., Kib-blewhite E.J., MNRAS , (1988) 23913. Davies R.L., Efstathiou G., Fall S.M., Illingworth G.,Schechter P.L., ApJ , (1983) 4114. de Rijcke S., Michielsen D., Dejonghe H., Zeilinger W.W.,Hau G.K.T., A&A , (2005) 49115. Djorgovski S., Davis M., ApJ , (1987) 5916. D’Onofrio M., Capaccioli M., Caon N., MNRAS ,(1994) 52317. Ebisuzaki T., Makino J., Okumura S.K., Nature , (1991)21218. Emsellem E., et al., MNRAS , (2007) 40119. Faber S.M., et al., AJ , (1997) 177120. Falc´on-Barroso J., Peletier R.F., Balcells M., MNRAS ,(2002) 74121. Ferrarese L., et al., ApJS , (2006) 33422. Fisher D.B., Drory N., ApJ , (2010) 94223. Gadotti D.A., MNRAS , (2009) 153124. Gargiulo A., et al., MNRAS , (2009) 7525. Gavazzi G., Donati A., Cucciati O., Sabatini S., Boselli A.,Davies J., Zibetti S., A&A , (2005) 41126. Graham A.W., ApJ , (2004) L3327. Graham A.W., IAU Colloquia 198, “Near-Field Cosmologywith Dwarf Elliptical Galaxies”, H. Jerjen & B. Binggeli (eds.),(Cambridge, Cambridge University Press, 2005) 303-31028. Graham A.W., ApJ , (2008) 14329. Graham A.W., Driver S.P., PASA , (2005) 11830. Graham A.W., Erwin P., Trujillo I., Asensio Ramos A., AJ (2003) 191731. Graham A.W., Guzm´an R., AJ , (2003) 293632. Graham A.W., Merritt D., Moore B., Diemand J., Terzi´c B.,AJ , (2006) 271133. Graham A.W., Onken C.A., Athanassoula E., Combes F.,MNRAS, submitted (2010, arXiv:1007.3834)34. Graham A.W., Spitler L.R., MNRAS (2009) 214835. Graham A.W., Trujillo I., Caon N., AJ (2001) 170736. Graham A.W., Worley C.C., MNRAS , (2008) 170837. Greene J.E., Ho L.C., Barth A.J., ApJ , (2008) 15938. Held E.V., de Zeeuw T., Mould J., Picard A., AJ , (1992)85139. Jerjen H., Binggeli B.,
The Nature of Elliptical Galaxies;The Second Stromlo Symposium (ASP Conf. Ser. 1997), v.116,p.23940. Kormendy J., ApJ , (1977) 33341. Kormendy J., ApJ , (1985) 7342. Kormendy J., Fisher D.B., Cornell M.E., Bender R., ApJS , (2009) 21643. Krajnovi´c D., et al., MNRAS, (2008) 9344. La Barbera F., Covone G., Busarello G., Capaccioli M.,Haines C.P., Mercurio A., Merluzzi P., MNRAS , (2005)111645. Matkovi´c A., Guzm´an R., MNRAS , (2005) 28946. Merritt D., Milosavljevi´c M., Living Reviews in Relativity ,(2005) 847. Metcalfe N., Godwin J.G., Peach J.V., MNRAS , (1994)43148. Peletier R.F., Davies R.L., Illingworth G.D., Davis L.E.,Cawson M., AJ , (1990) 109149. S´ersic J.-L., Atlas de Galaxias Australes (Cordoba: Observa-torio Astronomico, 1968)50. Skelton R.E., Bell E.F., Somerville R.S., ApJ , (2009) L951. Stiavelli M., Miller B.W., Ferguson H.C., Mack J., WhitmoreB.C., Lotz J.M., AJ , (2001) 1385 52. Tolstoy E., Hill V., Tosi M., 2009, ARA&A, 47, 37153. Trujillo I., Erwin P., Asensio Ramos A., Graham A.W., AJ , (2004) 191754. Wolf J., Martinez G.D., Bullock J.S., Kaplinghat M., GehaM., Mu˜noz R.R., Simon J.D., Avedo F.F., MNRAS , (2010)122055. Young C.K., Currie M.J., MNRAS , (1994) L1156. Young C.K., Currie M.J., MNRAS , (1995) 114157. Zaritsky D., Gonzalez A.H., Zabludo ff A.I., ApJ638