Table Of ContentMon.Not.R.Astron.Soc.000,000–000(0000) Printed28January2013 (MNLATEXstylefilev2.2)
Classification and analysis of emission-line galaxies using
mean field independent component analysis
James T. Allen,1,2(cid:63) Paul C. Hewett,1 Chris T. Richardson,3 Gary J. Ferland4 and
Jack A. Baldwin3
3 1Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA
1 2Sydney Institute for Astronomy, University of Sydney, 44–70 Rosehill St, Redfern, NSW 2016, Australia
0 3Physics & Astronomy Department, Michigan State University, East Lansing, MI 48824-1116, USA
2 4Physics & Astronomy Department, University of Kentucky, Lexington, KY 40506-0055, USA
n
a
J 28January2013
4
2
ABSTRACT
] We present an analysis of the optical spectra of narrow emission-line galaxies, based
O
on mean field independent component analysis (MFICA), a blind source separation
C technique. Samples of galaxies were drawn from the Sloan Digital Sky Survey (SDSS)
. andusedtogeneratecompactsetsof‘continuum’and‘emission-line’componentspec-
h
tra. These components can be linearly combined to reconstruct the observed spectra
p
of a wider sample of galaxies. Only 10 components – five continuum and five emis-
-
o sion line – are required to produce accurate reconstructions of essentially all narrow
r emission-line galaxies to a very high degree of accuracy; the median absolute devia-
t
s tions of the reconstructed emission-line fluxes, given the signal-to-noise ratio (S/N)
a
of the observed spectra, are 1.2–1.8σ for the strong lines. After applying the MFICA
[
components to a large sample of SDSS galaxies we identify the regions of parameter
1 space that correspond to pure star formation and pure active galactic nucleus (AGN)
v emission-line spectra, and produce high S/N reconstructions of these spectra.
0 The physical properties of the pure star formation and pure AGN spectra are
3 investigated by means of a series of photoionization models, exploiting the faint emis-
9
sion lines that can be measured in the reconstructions. We are able to recreate the
5
emission line strengths of the most extreme AGN case by assuming the central en-
.
1 gine illuminates a large number of individual clouds with radial distance and density
0 distributions, f(r) ∝ rγ and g(n) ∝ nβ, respectively. The best fit is obtained with
3 γ = −0.75 and β = −1.4. From the reconstructed star formation spectra we are able
1
to estimate the starburst ages. These preliminary investigations serve to demonstrate
:
v thesuccessoftheMFICA-basedtechniqueinidentifyingdistinctemissionsources,and
i its potential as a tool for the detailed analysis of the physical properties of galaxies in
X
large-scale surveys.
r
a Keywords: methods:dataanalysis–galaxies:active–galaxies:evolution–galaxies:
nuclei – galaxies: star formation – galaxies: statistics
1 INTRODUCTION techniques that make use of all available data are required
in order to obtain a more detailed picture of the physical
Theopticalandultravioletemission-linespectraofgalaxies
properties and evolution of galaxies.
have proven to be a valuable source of information regard-
The classification and analysis of active galactic nu-
ingthephysicalconditionsthatprevailwithinsuchobjects.
clei(AGN)andstarformation(SF)innarrowemission-line
However,themajorityofdiagnosticsandanalysistechniques
galaxies is one area in which updated analysis techniques
currently in use focus on measurements of a few small re-
have the potential to provide new insights into the physi-
gions of each spectrum, discarding the remaining informa-
calprocessesthatgoverntheseobjects.Thewell-established
tion.Withthegreatlyincreasedqualityandquantityofdata
correlations between the properties of supermassive black
madeavailablebyrecentextragalacticsurveys,newanalysis
holes(SMBHs)andthoseoftheirhostgalaxies(e.g.Magor-
rian et al. 1998; Ferrarese & Merritt 2000; Kormendy &
(cid:63) E-mail:[email protected] Gebhardt2001;Ha¨ring&Rix2004)suggestastrongevolu-
(cid:13)c 0000RAS
2 J. T. Allen et al.
tionary link between the two. Feedback processes, in which tra. The most familiar BSS technique applied to astronom-
galaxy-scalewindspropelledbytheAGNheatandexpelthe ical spectra is principal component analysis (PCA), which
interstellarmedium,shuttingdownbothstarformationand hasseenuseformorethantwodecades(Mittazetal.1990;
furtherblackholeaccretion,areofteninvokedtoexplainthis Francisetal.1992;Yipetal.2004).WhilethePCA-derived
link (e.g. Granato et al. 2004; Springel, Di Matteo & Hern- component spectra can be used to provide approximations
quist 2005; Croton et al. 2006). Direct tests of such models to the object spectra, the interpretation of the individual
have proved challenging, although some progress has been component spectra themselves has only rarely proved illu-
made in measuring the time delays between star formation minating.Themoreambitiousgoalistogeneratecomponent
andAGNactivity(Schawinskietal.2007;Wildetal.2010), spectra that relate to the underlying physical constituents
allowing a comparison to the feedback timescales predicted withinagalaxywhichcanbeanalysedusingstandardtech-
by the simulations. niques to determine the physical conditions contributing to
In order to investigate the relationship between AGN the individual components.
and SF across modern large-scale surveys, a necessary first Morerecently,otherBSStechniqueshavebeenapplied
step is to accurately identify each process. The most com- totheanalysisofUV/opticalspectra,includingindependent
monlyusedmethodstodistinguishAGNfromSFinoptical component analysis (ICA; Lu et al. 2006) and non-negative
spectra date back to the work of Baldwin, Phillips & Ter- matrix factorisation (NMF; Blanton & Roweis 2007; Allen
levich (1981, hereafter BPT) proposing the use of a num- etal.2011).Herewepresentanapplicationofmeanfieldin-
beroflineratiodiagrams,inparticular[Oiii]λ5008/Hβ vs. dependent component analysis (MFICA), a BSS technique
[Nii]λ6585/Hα,toestablishtheionizingsourcepoweringan previously unused in astronomy, to the analysis of SDSS
observed emission-line spectrum. Additional line ratio dia- spectra. MFICA is applied to a sample of narrow emission-
grams were introduced by Veilleux & Osterbrock (1987). linegalaxies,generatingasmallnumberofcomponentspec-
Subsequent advances in photoionization modelling, tra that, along with a corresponding set of weights, can be
combinedwiththelargedatasetsprovidedbytheSloanDig- usedtoreconstructthespectrumofeachobjectinthesam-
italSkySurvey(SDSS;Yorketal.2000),haveallowedmore ple.Thisapproachallowsforthestraightforwardidentifica-
quantitative BPT-based classifications to be made. In par- tion of spectra corresponding to pure SF and pure AGN,
ticular, diagnostic lines were defined in the BPT plane by as well as the generation of high signal-to-noise ratio (S/N)
Kewley et al. (2001) and Stasin´ska et al. (2006), based on examples of such spectra, which in turn can be analysed to
photoionization modelling, while Kauffmann et al. (2003) determine their detailed physical properties.
presented an empirical classification based on a large sam- TheprimarygoalofthispaperistodescribetheMFICA
ple of galaxies from the SDSS. Kewley et al. (2006) further techniqueandhowtheMFICAspectralcomponentscanbe
extended these schemes by defining the region between the used to trace physically-significant trends, parametrized as
Kewley et al. (2001) and Kauffmann et al. (2003) lines as loci, in the spectra of large samples of emission-line galax-
the ‘composite’ region, in which each galaxy is expected to ies.WediscussourresultsfortheSDSSsampleprimarilyto
hostbothSFandanAGN.Manyrelateddiagnosticmethods illustrate the method and assess how well it works. In Sec-
havebeenproposedthatmakeuseofavarietyoflineratios, tion2weintroduceMFICA,andinSection3wedescribethe
in some cases combining these with other properties of the galaxy samples used. Section 4 describes the methods used
galaxies (e.g. Diaz, Pagel & Wilson 1985; Osterbrock, Tran togeneratecomponentspectra,fitthesecomponentstoob-
& Veilleux 1992; Lamareille et al. 2004; Lamareille 2010; served spectra, and identify the regions of parameter space
Marocco,Hache&Lamareille2011;Yanetal.2011;Juneau corresponding to SF and AGN. In Section 5 we present our
et al. 2011). results, including a preliminary investigation of the physi-
Notwithstanding the undoubted success of the BPT- cal properties of galaxies within the SF and AGN regions.
based diagnostic methods in separating AGN-dominated We summarise our conclusions in Section 6. Vacuum wave-
fromSF-dominatedgalaxies,fixedboundariesandbi-modal lengths are used throughout the paper.
classifications are normally involved. In practice, for a wide
range of applications, we wish to quantify the contribution
from each source to each galaxy, over the full range from
2 MEAN FIELD INDEPENDENT
100percentAGNto100percentSF,includingthosecases
COMPONENT ANALYSIS
where only a weak contribution from one of the sources is
present.Suchmeasurementswillproveinvaluablein,forex- Blindsourceseparation(BSS)techniquesareusedtorewrite
ample,studiesofthefeedbackmechanismsthatrelatesuper- adatamatrix,V,astheproductofasetofcomponents,S,
massiveblackholepropertiestothoseoftheirhostgalaxies, and weights, A:
in which case a full census of SF and AGN properties will
V=AS. (1)
allowafarmoresensitiveanalysisoftheconnectionbetween
these two sources. Inthecontextofthiswork,Visann×marrayofflux
Inordertomakepossiblethesemoresensitivemeasure- measurements for n different galaxies at m wavelengths, S
ments, we must develop techniques that incorporate all the isanr×marrayofther componentspectraoverthesame
information contained within each optical spectrum. Addi- wavelengths, and A is an n×r array of the corresponding
tionally,informationfromalargenumberofspectrawithina weights for each galaxy. For any individual galaxy, the ob-
surveycanbecombinedandanalysedasasingleunit.Blind served spectrum is written as a linear combination of the r
sourceseparation(BSS)techniquesprocessdatainthisway, components. In the case that r < n, the equality in equa-
deriving sets of component spectra that can be combined tion 1 is an approximation, and the product AS can be
with varying weights to reconstruct each of the input spec- viewed as a reconstruction of the original data. The choice
(cid:13)c 0000RAS,MNRAS000,000–000
Analysis of emission-line galaxies using MFICA 3
ofr dependsonanumberoffactors,includingtheexpected
nature of the components, the S/N of the input data, and
the particular purpose of the analysis.
Mean field independent component analysis (MFICA;
Højen-Sørensenetal.2002;Opper&Winther2005)isaBSS
techniquethatproducesasmallnumberofcomponentsthat
can be used to provide reconstructions of the individual in-
put spectra. MFICA imposes a prior on the components,
P(S),andcombinesP(S)withtheerrorinthereconstruc-
tions to maximize the likelihood of the parameters:
(cid:90)
P(V|A,Σ)= dSP(V|A,Σ,S)P(S), (2)
where
P(V|A,Σ,S)=(det2πΣ)−N2 e−12Tr(V−AS)TΣ−1(V−AS),
(3)
whereN isthenumberofinputspectra,andΣisthenoise
covariance.Σdoesnotneedtobespecifiedinadvance,and
is calculated from the data along with A and S. The pa-
rametersAandSprovideafulldescriptionofthenoise-free
spectra, while Σ describes the noise in the observations. In
thiswork,Σistakentobeascalar.Inessence,MFICAde-
rives a combination of A, S and Σ that combine to explain Figure 1.Positionsoftheinputsamplesinthe[Oiii]λ5008/Hβ
the input data V, while preferentially selecting values for vs. [Nii]λ6585/Hα BPT plane. Small grey points represent the
the individual pixels in S that maximize the chosen P(S). complete emission-line galaxy sample, while large black points
represent those galaxies used to generate the emission-line com-
Note that unlike many ICA techniques, MFICA does not
ponents. The solid and dashed red lines represent the classifica-
address the issue of statistical independence.
tioncurvesdefinedinKauffmannetal.(2003)andKewleyetal.
ThepriorP(S),whichcaninprincipletakealmostany
(2001),respectively.
form, can be used to place constraints on the components.
Restrictions can also be placed on the mixing matrix, A.
In particular, A and S can both be constrained to be non-
restrictedtoobjectswithanHαwidth1.9˚A(cid:54)σ <3.5˚A,
negative; such a constraint is appealing in the context of Hα
and objects with a visually-detected broad component to
spectroscopic observations where the physical emission sig-
theirHαemissionwereremoved.Theresultingsamplecon-
natures are expected to obey such a restriction naturally.
sists of galaxies with emission lines detected at moderate
S/N,andvelocitywidthsintheinterval(cid:39)120−330kms−1,
i.e.includingL∗andbrightergalaxies.Theirpositionsinthe
3 GALAXY SAMPLE [Oiii]λ5008/Hβ vs. [Nii]λ6585/Hα BPT plane are shown
by the small grey points in Fig. 1.
SDSS DR7 (Abazajian et al. 2009) galaxy samples at red-
Asampleofgalaxieswithoutemissionlineswasselected
shiftz(cid:39)0.1 providelarge numbers ofspectra,with moder-
from those with Hα detected in absorption with S/N(cid:62)3.0
ate S/N, covering a restframe wavelength interval that in-
cludes [Oii]λ3728 in the blue, through to [Ariii]λ7137 in and no detected emission in [Oii]λ3728 or [Oiii]λ5008. A
slightlybroaderredshiftrange,0.09(cid:54)z<0.13,wasusedto
thered.Anarrowredshiftintervalatz(cid:39)0.1wasthuscho-
increase the number of objects.
senfortheapplicationofMFICAtoinvestigatetheproper-
Beforeanyfurtherprocessingwascarriedoutthespec-
ties of narrow emission-line galaxies.
tra were sky-subtracted using the algorithm presented by
More specifically, a large sample of SDSS-classified
galaxies was selected with redshifts 0.10 (cid:54) z < 0.12.1 The Wild & Hewett (2005), which greatly improves the S/N at
observed wavelengths > 7200˚A. All spectra were corrected
redshift range is sufficiently broad that a large sample of
∼104 galaxies is available, while retaining a large common for Galactic dust reddening using the E(B−V) measure-
ments from Schlegel, Finkbeiner & Davis (1998) and the
rest-frame wavelength range for analysis. The spectra were
Milky Way extinction curve of Cardelli, Clayton & Mathis
also required to have at least 3800 ‘good’ pixels, defined as
(1989).
those for which the SDSS noise array is non-zero, and an
r-band S/N of 15.0(cid:54)SN R<30.0. Thegenerationofcomponentsrequiresanaccuratecor-
rection to rest-frame wavelengths, and is sensitive to sub-
Emission-line galaxies were selected to have positive
pixel errors in this correction. For the emission-line galax-
equivalentwidth(EW),indicatingemission,foreachofHβ,
[Oiii]λ5008, Hα and [Nii]λ6585, with S/N (cid:62) 5.0 for the ies,redshiftswereremeasuredbyfittingasetofthreeGaus-
flux measurements of Hβ and [Nii]λ6585. The sample was sians to the [Nii]λλ6550,6585 and Hα lines, after a prelim-
inary continuum subtraction. As the primary focus of this
work is the emission line spectrum rather than the under-
1 Objectsintherange0.111(cid:54)z<0.116werediscarded,because lying continuum, the Hα redshift was adopted as the sys-
ofthecoincidenceofthestrong5578.5˚Asky-linewithrest-frame temic redshift. For the galaxies without emission lines, the
[Oiii]λ5008inthegalaxies. SDSS redshift measurements – derived by cross-correlating
(cid:13)c 0000RAS,MNRAS000,000–000
4 J. T. Allen et al.
the spectra with a series of templates – were used. The Recognisingtheimportanceofaccuratecontinuumsubtrac-
sky-subtracted spectra were shifted to their respective rest tion in order to measure weak emission-line fluxes, a series
frames, interpolating between the SDSS pixels to ensure a of tests that probe that accuracy of the MFICA-based con-
precise rest-frame shift. A common rest-frame wavelength tinuum reconstructions are described in Section 4.2. The
range of 3500˚A<λ<8100˚A was retained. continuum-subtracted spectra were then used to generate a
set of five MFICA components that can be combined to-
gethertodescribetheemissionlinespectrumofanygalaxy,
3.1 Sample selection for component generation including both AGN and SF galaxies (Section 4.3). The
individual components do not represent distinct physical
Subsetsofthegalaxysamplearerequiredforthegeneration
sources; rather, they are high S/N representations of spec-
oftheMFICA-derived‘continuum’and‘emission-line’com-
troscopic traits that appear in galaxy spectra, and which
ponents. The number of spectra required depends on the
include weaker emission lines that are now largely free of
numberofcomponentspresentintheobjectpopulationand
contamination by the underlying galaxy.
the S/N of the spectra.
The five continuum and five emission-line components
The continuum components were derived using a were then fitted to each individual galaxy spectrum in the
modest-sizedsampleof170spectra.Thissamplesizeisade- fullsample(Section4.4).Theresultsofthisfittingallowus
quatebecauseonlyafewsuchcomponentswerebeingsought to characterise the emission-line properties of each galaxy
(Section 4.1). The galaxies were selected to include an ap- in a five-dimensional space, independent of the continuum
proximatelyevenspreadincontinuumcoloursbetweenblue properties. Finally, Section 4.5 describes the identification
and red, i.e. between young (post-starburst) and old (K- oftwolociofgalaxiesrunningthroughthisfive-dimensional
giant dominated) stellar populations. space.OnelocusisidentifiedwithSFgalaxies,andtheother
The galaxy emission-line properties exhibit a greater withAGN.Thepositionofagalaxywithinoneoftheseloci
variation, requiring a somewhat larger sample of galaxies. is determined by its emission-line properties, and hence by
The first stage in their selection was to place the objects in the underlying physical properties of that particular SF or
a classical [Oiii]/Hβ vs. [Nii]/Hα BPT diagram. Galaxies AGN galaxy.
were then selected with probability inversely proportional
to the local density of galaxies in the BPT diagram, pro-
ducing a sample evenly populating the occupied portion of 4.1 Generating continuum components
the diagram. Application of somewhat tighter constraints
In principle, given enough galaxy spectra of extremely high
on the spectrum S/N (16.0 (cid:54) SN R < 23.0) and the Hα
S/N and resolution, a BSS analysis should produce compo-
emission-linewidth(1.9˚A(cid:54)σ <3.0˚A)resultedinasam-
Hα nents that correspond to stellar spectral types that make
ple of 727 galaxy spectra. Their positions in the [Oiii]/Hβ
up loci of different ages and metallicities in a Hertzsprung-
vs.[Nii]/HαBPTplaneareshownbythelargeblackpoints
Russelldiagram.Morerealisticallythegoalforspectraofthe
inFig.1.Theoriginalsampleconsistedof730galaxiesbut,
qualityintheSDSSistheidentificationofcomponentsthat
following visual inspection, three galaxies with significantly
represent current star formation (O/B-star dominated), in-
dustreddenedcontinuawereremoved.Thepresenceofdust
termediate age (post-starburst, A-star dominated) and old
reducestheobservedfluxbyawavelength-dependentfactor;
(K-giantdominated),possiblywithsomeadditionalagedis-
althoughtheMFICAanalysisisabletoaccountformoder-
crimination for the intermediate age star-formation signa-
atelevelsofdust,themostextremeobjectscannolongerbe
tures.
described accurately by equation 1 and so are not included
Emission-line galaxies on their own are unsuitable for
in the component generation.
deriving continuum components as the emission lines co-
All the spectra used in the component generation were
incide with important features in the underlying stellar
normalisedaccordingtotheirmedianflux,topreventasmall
spectrum. This problem is particularly pronounced for the
numberofbrightgalaxiesfromdominatingthecomponents.
Balmerserieslines,whichareseenasstrongabsorptionfea-
tures in a range of main sequence stars. However, galaxies
with no emission lines also produce unsatisfactory contin-
uum components, as they do not include significant contri-
4 METHOD
butions from young O/B stars. In general, a sample that
MFICA was used to generate components from subsets of does not include a significant contribution due to star for-
theSDSSsample,andthesecomponentswerethenfittedto mation of all ages will not allow a BSS analysis to generate
the full sample of galaxies in order to study their contin- components that successfully reconstruct the full range of
uumandemission-lineproperties.Theanalysisisdescribed star-formation ages.
in detail in the following subsections; a brief overview is Here, such limitations affecting the identification of
given here. First, a set of five continuum components was continuum components representing all star-formation ages
generated from a combination of galaxies with and with- werecircumventedbyusingamixedsampleofgalaxieswith
out detected emission lines (Section 4.1). The components and without emission lines. First, a set of 20 emission-line
were constructed in such a way as to avoid contamination galaxies,withparticularlystrongcontributionstotheircon-
by emission lines, allowing them to be used to reconstruct tinua from young stars, was selected using a preliminary
and subtract the stellar continuum in SDSS galaxy spec- MFICA analysis. A set of two MFICA components, which
tra. Subtracting the continuum in this manner allows us to were very similar in form to the top two components in
isolate each galaxy’s emission-line spectrum with minimal Fig.2,wasgeneratedfromthe170galaxieswithoutemission
contamination from underlying stellar absorption features. lines,andfittedtothe727galaxieswithemissionlines.The
(cid:13)c 0000RAS,MNRAS000,000–000
Analysis of emission-line galaxies using MFICA 5
20 selected were those with the highest fractional contribu-
Table 1.Parametersusedtointerpolateoverfeaturesincontin-
tion from the component corresponding to a young stellar uumcomponents.
population. These 20 galaxies were added to the sample of
170galaxieswithoutemissionlines.Theselectionofgalaxies Component Feature λmin (˚A) λmax (˚A) Npix
with strong young-star contributions allowed a significant
[Oiii] 4955.1 4967.6 15
signal from such stars to be included in the sample with
[Oiii] 5000.9 5012.5 15
only a small number of emission-line galaxies, ensuring the
2 Hα 6563.7 6568.3 1
greatmajorityofgalaxiesinthesamplestillhadnodetected
[Nii] 6578.8 6589.5 1
emission lines. [Sii] 6715.1 6736.7 15
A set of seven components was generated from the
mixed sample, using the exponential prior: CaK 3927.8 3939.6 15
Hβ 4836.7 4892.7 15
3
P(S)=ηexp(−ηS)Θ(S), (4) Hα+[Nii] 6544.1 6591.0 15
[Sii] 6704.2 6719.7 15
where Θ(S) is the Heaviside step function and η is a di-
mensionless parameter, taken in this case as η = 1. This
priorwasselectedasitiszerofornegativevaluesofS,soit
produces non-negative component spectra, suitable for the
characterisationofemissionsources.Providedthiscondition respectively),althoughthethirdofthesecomponentsisrel-
issatisfied,theresultingcomponentsdonotdependstrongly ativelynoisy.TheOstarcomponentalsoshowsanincrease
on the form of the prior. The seven components could be influxtowardstheredfromapopulationofredsupergiants,
cleanly divided into three that were dominated by the stel- formedbytherapidevolutionofthemostmassivemainse-
lar continuum and four that were dominated by the emis- quence stars.
sion lines. The emission-line components were not used in Although these three continuum components are very
thefollowinganalysis–themethoddescribedinSection4.3 successfulinreconstructingthecontinuaofobservedgalaxy
produced emission-line components that could more easily spectra, some systematic low-level residuals remain. There
be analysed, and at higher S/N – but they played the role are two main effects that cause these residuals. First, as
of filtering out virtually all the emission-line signal, leav- a stellar population ages, its spectral energy distribution
ing the three continuum components almost entirely free of (SED) approximates a blackbody with successively lower
contamination by emission lines. temperatures, so its peak flux shifts to longer wavelengths.
Thenumberofcomponentsgeneratedatthispointwas Each of the three MFICA-derived continuum components
chosen to provide physically meaningful continuum compo- necessarily represents an average over a range of ages,
nents with a clean separation from the emission-line com- whereas the SED of individual galaxies can be dominated
ponents.Generatingfewercomponentscausessomecompo- by star formation of a particular age. Both very young
nents to show a combination of continuum and emission- and old stellar populations produce almost invariant signa-
line signatures, rather than being dominated by one or the tures in spectra with the S/N and resolution of the SDSS;
other.Generatingagreaternumberofcomponentsfromthis the question is essentially how much of each component
sample causes the continuum signal to be spread over more is present. By contrast, the signature of intermediate-age,
components in such a way as to obscure the clear physi- post-starburst, populations produces significant changes
cal interpretation discussed below, while providing only a with age as the dominant stellar type evolves from late B-,
minimal improvement in the accuracy of the resulting re- throughA-toearlyF-typestars,andthethreecomponents
constructions. The choice of seven components was made cannot fully reflect these changes on their own. The second
afterinspectingtheresultsfromarangeofnumbersofcom- effect is that the relative contributions of the three compo-
ponents. nentstoanindividualgalaxyislargelydrivenbytheoverall
The performance of the MFICA in terms of the de- shape of the SED but, for example, a red SED can result
gree of cross-talk between components is impressive. How- from an old stellar population with little dust, or from a
ever,thepresenceoftheveryhigh-contrast,narrowemission younger population with a higher level of dust reddening.
lines, combined withthe limitedS/N of thegalaxy spectra, The spectra of these two possibilities will differ in features
means that some low-level contamination of the continuum suchasthestrengthofthe4000-˚AbreakandtheBalmerab-
componentsbyresidualemissionfeaturesispresent.Specif- sorption lines and, as the MFICA approach used here does
ically, two of the three continuum-dominated components not explicitly account for dust reddening, these differences
showedsomecontamination,primarilyatthelocationofthe are not fully described by the existing three components.
strongestemissionlines.Theregionsofcontaminationwere Itwouldbepossibletoreducetheresidualstosomeex-
identified by visual inspection. A linear interpolation was tent by increasing the number of components generated at
then applied to produce the final continuum components. thefirststepdescribedabove.Thisapproachisnotfollowed
The parameters used in the interpolation are listed in Ta- here, for two reasons. Firstly, the resulting components can
ble 1; for each emission line the continuum between λ no longer be clearly identified with stellar populations of
min
and λ was set by interpolating between the median flux different ages, making investigations of the sort described
max
levels in the N pixels on either side of the region. in Section 5.1 more challenging. Secondly, a wider range of
pix
The top three spectra in Fig. 2 show the original com- galaxiescanbereconstructedbygeneratingadditionalcom-
ponents,aswellastheresultsafterinterpolation.Thethree ponents,tobeusedincombinationwiththefirstthree,from
components can be identified with old, intermediate and a sample that has a greater number of emission-line galax-
young stellar populations (dominated by K, A and O stars ies;theinclusionofsuchgalaxiesintheinputsampleensures
(cid:13)c 0000RAS,MNRAS000,000–000
6 J. T. Allen et al.
Figure 2. MFICA continuum components. Components are offset for clarity; dashed lines mark successive zero points. Components
1–3 were generated from a mixed sample of 170 galaxies without emission lines and 20 with emission lines; the final two ‘adjustment’
components, numbers 4 and 5, were generated from a mixed sample consisting of the same 170 galaxies without emission lines and
727galaxieswithemissionlines.Forcomponents1–3,thegreylinesshowtheoriginalcomponents,whiletheblacklinesshowthefinal
versionsafterinterpolatingoverasmallnumberofnarrowfeatures.
(cid:13)c 0000RAS,MNRAS000,000–000
Analysis of emission-line galaxies using MFICA 7
that the components are able to describe such galaxies. We
Table2.Wavelengthrangesmaskedwhengeneratingcontinuum
adopt this strategy here. adjustmentcomponents.
In order to reconstruct more accurately the spectra of
galaxies covering a wide range of stellar populations and Emissionline λmin (˚A) λmax (˚A)
levels of dust reddening, an additional set of ‘adjustment’
[Oii] 3719.5 3737.5
components was generated, using the 170 galaxies without
Hκ 3748.1 3755.3
emission lines and all 727 with emission lines. The original
Hι 3765.6 3775.1
three continuum components were fitted to the combined
Hθ 3794.8 3803.5
sample of 897 galaxies, with the emission-line wavelength
Hη 3831.3 3840.0
ranges listed in Table 2 masked out, using the MFICA al- [Neiii] 3865.9 3873.4
gorithm with the components held fixed.2 After subtract- Hei+Hζ 3883.5 3895.4
ing the initial three-component continuum fit, the masked [Neiii]+H(cid:15) 3964.6 3975.5
‘residual’spectrawereusedtogeneratefurtherMFICAcom- [Sii] 4066.4 4081.9
ponents. When combined with the ‘mean’ intermediate age Hδ 4098.5 4108.3
star-formation component, the new components allow the [Fev] 4225.5 4235.5
Hγ 4335.1 4347.8
generation of spectra corresponding to somewhat younger
[Oiii] 4358.8 4369.1
and older star formation.
Hei 4469.0 4476.5
The positivity constraints on these additional compo-
[Feiii] 4655.5 4663.2
nents and their weights were dropped, and a Laplace prior Heii 4683.1 4690.9
was used, defined as [Ariv] 4708.8 4716.6
η [Ariv] 4737.5 4745.5
P(S)= exp(−η|S|), (5)
2 Hβ 4850.1 4879.0
[Oiii] 4949.9 4967.7
again with η = 1. The Laplace prior allows both positive
[Oiii] 4997.7 5019.2
and negative values, making it suitable for generating com- [Ariii]+[Ni] 5188.9 5207.0
ponentsthatareintendedtodescribedeviationsfromapre- [Cliii] 5514.6 5523.8
vioussetofpositivecomponents.Itwasfoundthatgenerat- [Cliii] 5534.6 5543.9
ingtwoadditionalcomponentswassufficienttofullyrecon- [Oi] 5574.2 5583.5
struct the observed continua, with any further components [Nii] 5751.4 5761.0
producing no significant improvement. Hei+NaD 5869.3 5904.5
The regions that had been masked out when the ad- [Fevii] 6082.9 6093.1
[Oi] 6296.8 6308.3
justmentcomponentsweregeneratedwereinterpolatedover,
[Siii] 6308.6 6319.1
usingasimplelinearinterpolation,toproducethefinalcom-
[Oi] 6360.2 6370.8
ponents. The two ‘adjustment’ components are included in
Hα+[Nii] 6537.0 6598.2
Fig.2.Havingremovedthenon-negativityconstraint,these Hei 6673.4 6686.6
two components do not have clear physical interpretations. [Sii] 6708.2 6743.8
However, their presence does not negate the physical inter- [Ariii] 7130.8 7143.7
pretationsofthefirstthreecomponents,whichresultedfrom [Feii] 7150.2 7164.1
the enforcement of non-negativity at that stage. [Oii] 7315.9 7337.8
The continuum components were normalised such that [Ariii] 7746.7 7759.7
thesumofthesquaresoftheirpixelvaluesisequaltounity.
As noted above, dust reddening is not explicitly accounted
forinthereconstructions,butinpracticetherangeoflevels
features present. Weak emission lines, including [Nii], Hα,
of reddening in the input spectra allows a similar range to
[Oiii] and Hβ, do however, appear to be present. The posi-
be reconstructed successfully by the MFICA components.
tions of these features are marked in the RMS spectrum in
This point is discussed further in Section 5.1.
the bottom panel of Fig. 3.
Theemission-linesignatureis,atfirstsight,unexpected
4.2 Accuracy of the continuum components giventheinputgalaxysamplewasdeliberatelychosentobe
freeofgalaxieswithdetectableemission.Insightintotheori-
TheeffectivenessoftheMFICAtechniqueinreconstructing
ginoftheweakemissionlineresidualscomesfromthedistri-
theunderlyinggalaxycontinuaandphotosphericabsorption
butionoftheEWoftheresidualsatthewavelengthsofemis-
is evident from consideration of the features present in the
sionlines,showninFig.4.Thedistributionconsistsof(cid:39)74
mean and root mean square (RMS) of the galaxy minus re-
percentofthegalaxiescentredonaresidualHα+[Nii]EW
constructions,forthe170galaxieswithoutdetectedemission
of0.8˚A((cid:39)1.5×10−16ergs−1cm−2),withatailof(cid:39)26per
lines(Fig.3).TheRMSiscalculatedafterscalingtheresid-
centofobjectspossessinglargerpositivefluxresiduals.The
uals by the SDSS noise arrays. The mean residual, shown
flux residuals in the tail are well in excess of the noise and
in the middle panel of Fig. 3, appears to show an essen-
a composite of the 26 per cent of galaxies with the largest
tially featureless continuum with no detectable absorption
residuals shows a weak, but high S/N, emission-line spec-
trumconsistentwithLINERfluxratios,withlog([Nii]/Hα)
2 In practice the procedure produces results almost identical to =0.13andlog([Oiii]/Hβ)=0.17.Thiscompositeisshown
performing a minimum χ2-fit of the three components to each in Fig. 5. For comparison, we note that Sarzi et al. (2006)
galaxyspectrum. found weak emission lines with Hβ EW in the range 0.1–
(cid:13)c 0000RAS,MNRAS000,000–000
8 J. T. Allen et al.
Figure 3. Top: mean normalised spectrum (black) of the galaxies without emission lines, and the corresponding mean MFICA recon-
struction (red). Middle: mean residuals after subtracting the MFICA reconstruction. Bottom: RMS of the residuals normalised by the
SDSS noise arrays. Features corresponding to known emission and absorption lines are labelled. Pixels with zero noise reported in the
SDSSspectrumwereremovedfromtheRMScalculation,aswasastrongartefactcoveringafurtherfourpixelsinoneofthespectra.
(cid:13)c 0000RAS,MNRAS000,000–000
Analysis of emission-line galaxies using MFICA 9
lines along with the emission lines. However, given the fi-
nite S/N of the individual spectra and very limited impact
on the emission-line properties we have not pursued such a
course.
The other feature due to absorption lines that appears
in the bottom panel of Fig. 3 as having an unusually high
RMSresidualistheMgbbandat5180˚A.Thisfeatureisof-
tenusedasanalpha-elementabundancetracer.Itisseento
be strong in one of the continuum adjustment components
(component4)showninFig.2,suggestingthatitsstrength
has a large scatter in our sample. The increased RMS indi-
cates that the continuum components do not fully account
forthisscatter.AsfortheNaDandCaiiH&Kfeaturesdis-
cussed above, the RMS residual at the wavelength of Mgb
couldinprinciplebedecreasedbyincreasingthenumberof
components used. Again, we have not done so due to the
very limited benefit that would be gained.
We note the absence of increased RMS in the wings
Figure4.HistogramoftheEWoftheresidualsintheHα+[Nii] of absorption features. The RMS peaks for the interstel-
spectral region, for the 170 galaxies without detected emission lar features discussed above are no broader than the mean
lines. Objects with EW>1.5˚A, marked by the red dashed line, absorption features themselves, while photospheric absorp-
wereincludedinthemeanresidualspectrumshowninFig.5. tion features such as Feiλ5270 are not visible in the RMS
spectrum at all. As mentioned in Section 3, the definition
of the galaxy sample via a narrow range in spectrum S/N,
1.0˚AandlineratiosconsistentwithLINERstobecommon within a narrow redshift interval, means that the galaxies
in integral field observations of early-type galaxies. possessarestrictedrangeofluminosityandhencemass.As
The clear emission line signature in the mean residual a consequence, the variation in galaxy velocity dispersion
spectrum thus derives from the presence of a fraction of is small and produces no detectable effect on the form and
early-type galaxies that possess weak emission line signa- effectivenessoftheMFICAcontinuumcomponentswhenre-
turesthateludetheSDSSemission-linedetectionalgorithm. producing photospheric absorption features. Had the input
Throughout the remainder of the wavelength range, away galaxy sample contained a wider range of velocity disper-
from the emission lines, the mean residual is, as expected, sions,thelimitationsoftheMFICAapproachinaccounting
very small, not exceeding 0.5 per cent of the continuum for different widths of features would have been expected
level.Thepresenceofthesub-sampleofemission-linegalax- to manifest itself in an increased RMS in the wings of the
iesisalsoresponsiblefortheexcessRMSattheemission-line absorption features.3
wavelengthsvisibleinthegalaxy-minus-reconstructionRMS The accuracy of the continuum reconstructions in
plot. emission-line galaxies is illustrated in Fig. 6, which shows
The RMS spectrum also displays a large increase in the mean continuum fit along with the mean residual and
amplitude coincident with the NaDλλ5869.3,5904.5 dou- theRMSoftheresidualsnormalisedbythenoise.Thesam-
blet and a less extreme increase coincident with the pleof727galaxiesusedtoproducetheemission-linecompo-
CaiiH&Kλλ3969.6,3934.8 doublet. The distribution of nents (Section 4.3) was used to generate these composites.
residuals for the individual galaxies in the sample (at the Asexpectedthereareverystrongresidualsatthepositions
wavelengths of at NaD and Caii) is centred on zero, and of known emission lines, but in the continuum regions the
shows the majority to possess no significant residuals. Five RMS residuals are similar to those for the galaxies with-
of the 170 galaxies (3 per cent) show much stronger ab- out identified emission lines, indicating the continuum re-
sorption than predicted by the continuum reconstructions. constructions are as accurate as can be expected given the
Theabsorptionsignaturecorrespondstothestrongresonant observational noise.
transitionsfromspeciesthatdominatetheopticalspectrum Attheemission-linepositionslistedinTable2theaccu-
of cool atomic gas in the interstellar medium of galaxies racy of the continuum components will be impacted by the
(Draine 2011). Many of the genuine early-type galaxies in masking and interpolation used in their generation. To test
the ‘continuum’ galaxy sample do not possess cool atomic the subsequent effect on the emission-line components, the
interstellar medium, but the later-type galaxies (S0s and continuum components were recalculated 150 times, follow-
early-type spirals without current star-formation) do pos- ing the procedure described in Section 4.1. For each of the
sessinterstellargasthatmanifestsitselfviaabsorption.The 150 repeats, an additional masked region 10-˚A wide, cho-
limited number of continuum MFICA components are un- sen at random from the regions not already masked, was
able to reproduce the additional absorption, the observa-
tional signature of which is just a small number of discrete
3 If the continuum component definition is undertaken using
absorption(negative)featuresinasmallminorityofthein-
a galaxy sample with a significant range of velocity-dispersion,
put galaxies. It would be possible in principle to generate
or the continuum components are to be applied to galaxies
an ‘absorption’ component using the MFICA by increasing with a significant range of velocity dispersion, galaxy spectra of
thenumberofcomponentsforwhichthenon-negativitycon- continuum-components can be pre-smoothed as per the scheme
straint is not used, and taking care not to mask absorption fortheemissionlinesdescribedinSection4.3.
(cid:13)c 0000RAS,MNRAS000,000–000
10 J. T. Allen et al.
Figure5.Meanresidualspectrum,normalisedtothemediancontinuumlevel,ofthe26percentofgalaxieswiththestrongestresiduals
around Hα, from the sample without identified emission lines. The lower panels show the regions around Hβ (left) and Hα (right) in
moredetail,showingLINER-likeemission-lineratios.
added to the list in Table 2. The resulting continuum com- thefourthandfifthcontinuumcomponentsweregenerated.
ponents were fitted to and subtracted from the sample of The resulting emission-line components, shown in the left
727emission-linegalaxies,whichwerethenusedtogenerate panels of Fig. 7, are then seen to deviate from the median
new emission-line components following the procedure de- values in this region. As a result, the model spectra in the
scribedinSection4.3.Forsimplicity,themedianfilteringto right panels also deviate from the median levels. However,
remove the low-level positive offset described in Section 4.3 the error introduced by this mask is very small relative to
was not performed; doing so has a negligible effect on the thepeakfluxinthecomponentsandmodels.Combiningthe
emissionlinemeasurements.Inordertomeasurethepoten- 4×150 = 600 flux measurements from all runs, the mean
tialeffectofthemaskingprocedureonanemissionline,four changeinfluxrelativetoHβ is2.0×10−3,withastandard
model spectra were generated from each of the 150 sets of deviation of 6.3×10−3. Hence the error in the measured
emission-line components by combining them with weights emission line fluxes, introduced by the masking and inter-
correspondingtoeachendofthestar-formingandAGNloci polation carried out during the continuum component gen-
describedinSection4.5,i.e.thepointss0,s2,a0anda2de- eration, is constrained to be less than 1 per cent of the Hβ
fined in that Section. ‘Median components’ were calculated flux.
by taking the median value across the 150 realisations of
Accuratereconstructionofthegalaxycontinuaatloca-
each component at each pixel. These median components
tions such as the Balmer series wavelengths is of particular
were also combined using the same sets of weights to pro-
importance,andismademorechallenging,duetothesuper-
duce‘medianmodels’,whichwereusedasabaselineagainst
positionofstrongemissionandabsorptionfeatures.Wetest
which to measure the effect of the additional masks. The
the accuracy of the MFICA Balmer absorption reconstruc-
change in the flux within the extra 10-˚A mask, relative to
tionsbymeasuringtheHβabsorptionEW,definedusingthe
the median models, was measured and normalised by the
Lick indices (Worthey et al. 1994), from the continuum re-
Hβ flux; this change in flux was taken as a measure of the
constructionsforthefullsampleof∼104emission-linegalax-
effect of the mask on the flux of a coincident emission line.
ies(seeSection4.4foradescriptionoftheprocessoffitting
Anexamplesetofemissionlinecomponentsandmodel the components to observed spectra). By measuring from
spectra is shown in Fig. 7. In the example shown, the re- the continuum reconstructions, which by definition do not
gion between 7235.2 and 7245.2˚A was masked out when include the emission lines, we examine the underlying ab-
(cid:13)c 0000RAS,MNRAS000,000–000
