The Balmer decrement of SDSS galaxies
aa r X i v : . [ a s t r o - ph . C O ] S e p Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 14 September 2011 (MN L A TEX style file v2.2)
The Balmer decrement of SDSS galaxies
Brent Groves ⋆ , , Jarle Brinchmann , and Carl Jakob Walcher Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands Max Planck Institute for Astronomy, K¨onigstuhl 17, D-69117 Heidelberg, Germany Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
14 September 2011
ABSTRACT
High resolution spectra are necessary to distinguish and correctly measure the Balmer emis-sion lines due to the presence of strong metal and Balmer absorption features in the stellarcontinuum. This accurate measurement is necessary for use in emission line diagnostics, suchas the Balmer decrement (i.e. H α / H β ), used to determine the attenuation of galaxies. Yet athigh redshifts obtaining such spectra becomes costly. Balmer emission line equivalent widthsare much easier to measure, requiring only low resolution spectra or even simple narrow bandfilters and therefore shorter observation times. However a correction for the stellar contin-uum is still needed for this equivalent width Balmer decrement. We present here a statisticalanalysis of the Sloan Digital Sky Survey Data Release 7 emission line galaxy sample, usingthe spectrally determined Balmer emission line fluxes and equivalent widths. Using the largenumbers of galaxies available in the SDSS catalogue, we determined an equivalent widthBalmer decrement including a statistically-based correction for the stellar continuum. Basedon this formula, the attenuation of galaxies can now be obtained from low spectral resolu-tion observations. In addition, this investigation also revealed an error in the H β line fluxes,within the SDSS DR7 MPA / JHU catalogue, with the equivalent widths underestimated byaverage ∼ A V , and futureanalyses of this sample need to include this correction. Key words: galaxies: starburst – galaxies: statistics – galaxies: active – dust, extinction
The Balmer lines are the most well known and observed emissionlines in astronomy, being both strong lines in the optical and ubiq-uitous as they arise from recombination to the n = ff erencebetween the measured ratios of the Balmer lines and the intrinsicvalues expected can be used to determine the reddening of galaxies,or, more accurately, the ionized regions within them. In associationwith a attenuation / reddening-law and selective-to-total attenuation, R V , the reddening can then give the total attenuation of a galaxy(e.g. the oft used work of Calzetti 2001). This possibility of us-ing the hydrogen emission lines, in particular the ratio of the twostrongest Balmer lines H α and H β , to measure the reddening and at-tenuation has been known and utilized for many years (e.g. Berman ⋆ [email protected] ff ected by the path length through an absorbing medium).However, the accurate measurement of the Balmer decrement(i.e. the ratio of H α / H β ) requires the measurement of both the rel-atively weak H β line and the continuum underneath it to distin-guish the line. Separation of the underlying continuum from theBalmer emission lines is vital as the metal absorption lines and, es-pecially, Balmer absorption lines present in the spectrum of later-type stars act to weaken or hide the relative flux of the emissionlines in the integrated spectra of galaxies. Such was shown byLiang et al. (2004), where the H β line was not observed in a se-lection of galaxies in low-resolution spectra ( R = R > β lines hidden by both dustand absorption lines. The exposure times needed to obtain su ffi -cient spectral resolution to distinguish the emission lines from theunderlying stellar continuum of galaxies means that studies of theBalmer decrement tend to be biased to high emission-line equiva-lent width objects. While this bias may not be a serious issue, withdustier, more attenuated objects tending to have higher specific starformation rates and thus higher emission line equivalent widths (seee.g. da Cunha et al. 2010), such biases do tend to limit samples for B. Groves, J. Brinchmann, & C.J. Walcher investigations of dust and star formation. This is especially so athigher redshifts where the high spectral resolution needed to re-solve both the line and continuum limits surveys to the brightestobjects.Even with moderate resolution spectra, the Balmer emissionline fluxes are still sensitive to the way the stellar absorption isaccounted for, and this can be a substantial source of error, particu-larly for weak emission line sources.It is these issues that motivates us to examine the possibil-ity of determining the decrement from the equivalent widths of theBalmer emission lines. Emission line equivalent widths do not re-quire high resolution spectra to distinguish the line from the contin-uum, allowing the use of low resolution spectra, such as at R ∼ ∼ NIRSpec on JWST, the in-fluence of H β on the interpretation of galaxy spectra can still besignificant (Pacifici et al., in prep), and the line is still detectable ata signal-to-noise ∼ R < ii ] λ α ,not detecting the lines.To examine how the Balmer line equivalent widths can be usedto determine the Balmer decrement we use the Sloan Digital SkySurvey (SDSS Abazajian et al. 2009), which contains a large spec-troscopic sample of emission line galaxies covering a wide rangeof galaxy types and properties, including attenuations. With sucha wide range of galaxies, and reasonably high resolution spectra( R ∼ / JHU catalogue used here) and(Lamareille et al. 2006, applied this to lower resolution, higher red-shift data in the VVDS sample), pPXF (Cappellari & Emsellem2004), STARLIGHT (Cid Fernandes et al. 2005), STECKMAP(Ocvirk et al. 2006), and VESPA (Tojeiro et al. 2007), all use lin-ear combinations of synthetic stellar population spectra (such asfrom Bruzual & Charlot 2003) to fit the full observed spectra ofgalaxies using various optimized maximum likelihood approaches.These codes have been created to extract the maximum possibleinformation from galaxy spectra given degeneracies and noise (seee.g. the discussion in Ocvirk et al. 2006), and thus are clearly thebest approach when strong continuum is detected. Yet the amountof possible information to be extracted reduces with both decreas-ing signal-to-noise ratio and spectral resolution. In addition, thesemethods are limited by the available spectral libraries, which maynot cover the full parameter range needed to match the observedgalaxies, and may have intrinsic issues, as we demonstrate here inan issue we discovered in the course of this paper. Thus an em-pirical method as we explore here is fully complementary to thespectral synthesis methods used in most works.In the following sections we introduce the Balmer lines, bothin absorption and emission ( § §
3, provide a possible way to determine the Balmer decre-ment from the equivalent widths( § λ (Å) 5000K 10,000K 20,000 KH α β γ δ Table 1.
Balmer lines, including rest-frame wavelengths (Air), and theirratios relative to H β for n e = cm − and 3 di ff erent temperatures ([valuesfrom Dopita & Sutherland (2003), based on data from Storey & Hummer(1995)). interesting problem with the fitting of the stellar continuum in theSDSS ( § The Balmer emission lines in the interstellar medium arise predom-inantly from the recombination and subsequent cascade of elec-trons to the n = n = α (i.e. transitionsto n = n = α and higherorder lines, such as the Balmer lines. These two cases will lead todi ff erent intrinsic ratios for the Balmer lines, with variations of thesame order as temperature e ff ects (for other possible “Cases” ofemission which may occur, see e.g. Ferland 1999; Luridiana et al.2009). While Case B is typically assumed for determining intrinsicratios, in reality the ratio in typical H ii regions lies between thesetwo cases, and must be determined using radiative transfer codessuch as MAPPINGS iii (see eg Groves et al. 2004) or CLOUDY(Ferland et al. 1998).In Table 1 we present the four strongest Balmer emission linesand their ratios relative to H β assuming Case B conditions. Theseratios are only weakly sensitive to density, with the H α / H β ratio at T = K equal to 2.86, 2.85, and 2.81 for the electron densitiesn e = , 10 , and 10 cm − respectively, hence we only show thelarger variation due to temperature here. For a full ratio descrip-tion see Table B.7 in Dopita & Sutherland (2003), or Table 4.4 inOsterbrock & Ferland (2006). While these variations due to tem-perature and density are significant, they are still small relative tothe e ff ects of dust, as visible in the later sections, and hence strongdiagnostics for the amount of reddening experienced by an emis-sion line galaxy. he Balmer decrement of SDSS galaxies As discussed in the introduction, the fitting of the underlying stel-lar continuum is a vital step in determining line fluxes, especiallyfor hydrogen (e.g. Balmer) and helium recombination lines, whichhave underlying corresponding absorption lines. The Balmer ab-sorption lines arise from the absorption of light by hydrogen in theexcited n = ff ective temperature and grav-ity, as they require a significant fraction of hydrogen to be excited tothe n = ef f ∼ ∼
2Å to ∼
15Å with the maximum value occurring for starsaged around 500 Myr (i.e. dominated by the light from A & Fstars). In Figure 1 we show the variation of the equivalent widths(EW) respectively for simple stellar populations as a functionof age and metallicity (as labelled in the left hand of the fig-ure in the H δ diagrams). We compare the four strongest lines;H α , H β , H γ , and H δ , using four models to determine the equiv-alent widths as labelled in the upper right; the Bruzual & Charlot(2003, BC03) stellar population synthesis code using the MILES(S´anchez-Bl´azquez et al. 2006; Cenarro et al. 2007) and Stelib(Le Borgne et al. 2003) stellar spectral libraries, and the 2008 ver-sion of the Charlot & Bruzual (in prep, CB08) code with theMILES library. Also shown by the dashed lines are the resultsfrom Gonz´alez Delgado & Leitherer (1999). The weak dependanceon metallicity and the strong dependance on age, with the peakin EW at 0 . − α , H β , H γ , and H δ ) varying at most a factor of ∼ ff mann et al. 2003a; Gonz´alez Delgado & Leitherer 1999;Gonz´alez Delgado et al. 1999).Thus, as the equivalent widths of the stellar absorption fea-tures are approximately constant with wavelength while the rela-tive strength of the Balmer emission lines decrease rapidly withdecreasing wavelength (i.e. for the higher order lines), stellar ab-sorption a ff ects strongly the measurement of the Balmer decrementi.e. H α / H β , H γ / H δ . This is especially so for weak emission linegalaxies where the stellar absorption features are relatively strongerand only H α is seen in emission. This relative importance of thee ff ect of the stellar Balmer absorption on the emission lines is im-portant when considering the Balmer ratios, as discussed in latersections. Within this work we base our findings on the spectroscopic datafrom the seventh Data Release of the SDSS (DR7 Abazajian et al.2009), though we also refer to the fourth Data Release (DR4Adelman-McCarthy et al. 2006) as well when necessary. The SDSSused a pair of multi-fibre spectrographs with fibres of 3” diameter.In most galaxies the fibres were placed as close as possible to thecentres of the target galaxies. The flux- and wavelength-calibratedspectra cover the range from 3800 to 9200Å, with a resolution of R ∼ / JHU analy- δ H γ H β H α CB08+MILESBC03+MILESBC03+Stelib
Z=0.008051015 H δ H γ H β H α Z=0.00410 δ H γ H β H α Z=0.020 Age [yrs] E W [ Å ] Figure 1.
Equivalent widths (EW) of the four dominant Balmer lines,H α , H β , H γ , and H δ (as labelled), for simple stellar populations of vary-ing age and metallicity (increasing from top to bottom row, as markedon lower left in H δ figure). Three stellar synthesis models are consid-ered, as indicated by the colours in the key in the upper right; theBruzual & Charlot (2003, BC03) stellar population synthesis code usingthe MILES (S´anchez-Bl´azquez et al. 2006; Cenarro et al. 2007) and Stelib(Le Borgne et al. 2003) stellar spectra libraries, and the 2008 version ofthe Charlot & Bruzual (in prep, CB08) code with the MILES library. Thedashed line shows the results from Gonz´alez Delgado & Leitherer (1999). sis of the SDSS spectroscopic sample . This database contains, inaddition to the emission line fluxes, derived physical properties forall spectroscopically observed galaxies in the SDSS DR7. The pro-cedure for emission line measurement, detailed in Tremonti et al.(2004), was to correct the line fluxes for stellar absorption, fittinga non-negative combination of stellar population synthesis mod-els from Charlot & Bruzual (in prep., CB08) for the SDSS DR7release and Bruzual & Charlot (2003, BC03) for the SDSS DR4release . The best-fitting stellar population model also places con-straints on the star formation history and metallicity of the galaxy(see e.g. Gallazzi et al. 2005), and has been used to estimate stellarmasses and star-formation histories (Kau ff mann et al. 2003a).The equivalent widths of the Balmer lines we use here,also available as part of the MPA / JHU database (listed as (linename) reqw in the gal line data file), are computed from straightintegration over the continuum-subtracted bandpasses listed in ta-ble 2. Note that, by definition, emission lines have negative valuesof equivalent width but for clarity in the rest of the paper we assignall emission lines a positive value. The continuum in this case is es-timated using a running median with a 200 pixel window and doesnot properly account for stellar absorption. This measurement isrepresentative of the cases where a more accurate determination ofthe stellar continuum, as done with the MPA / JHU database, is not The data catalogues are available from The model spectra used were from an early version of the models and dif-fer from what will be eventually published. The di ff erences from BC03 areprimarily due to di ff erent treatment of TP-AGB stars and that the empiricalstellar library used was the MILES library rather than STELIB. The spectra are available as part of theGALAXEV package, which is can be obtained from . B. Groves, J. Brinchmann, & C.J. Walcher
Table 2.
Equivalent width bandpassLine Centre (Å) Lower bound (Å) Upper bound (Å)H δ γ β α possible, such as with low resolution or low S / N data, and helpscharacterize the e ff ects of stellar absorption on the lines.As we concentrate on emission line galaxies in this work, inparticular galaxies with measurable Balmer emission lines, we haveplaced cuts on the signal-to-noise (S / N) of the Balmer emissionlines using the uncertainties given by the MPA / JHU catalogue. Asdiscussed on the website, the listed uncertainties are formal, andlikely underestimates, thus we increase the uncertainty estimates onthe emission lines to take into account continuum subtraction un-certainties by the factors listed on the web site determined by com-parisons of duplicate observations within the SDSS sample. Specif-ically for the Balmer lines, we multiply the line flux uncertaintyestimates by a factor of 1.882. From the full SDSS emission linegalaxy sample we define three galaxy samples depending on thelines and ratios being examined; SN(H α ,H β ), SN(H α ,H β ,H γ ), andSN(H α ,H β ,H γ ,H δ ), where we require a S / N > α , H β , H γ , & H δ ). The S / N cutsare dominated by the weakest line in each sample due to the strongdecrease in relative flux for the higher order lines, thus the inclusionof each higher order line biases the samples to higher equivalentwidths of the H α emission line. As shown in figure 2, beginningfrom the full galaxy sample of SDSS DR7 ( ∼ ∼ α in emission), with a broad spread ofequivalent widths peaking at ∼
20Å (as measured from the localcontinuum, not corrected for stellar absorption). As each higherorder Balmer line is included, the sample rapidly decreases andis biased to higher equivalent widths, with the SN(H α ,H β ,H γ ,H δ )sample limited to ∼ α ) > α ,H β ) has ∼ α ,H β ,H γ ) has ∼ α ) in a galaxy spectrum can be considered a proxy forthe specific star formation rate (the current star formation rate rel-ative to the total stellar mass, sSFR = SFR / M ∗ ) of a galaxy, the biasin EW(H α ) means a bias to more “starforming” galaxies, whichmeans a bias to lower-mass, lower-metallicity, bluer galaxies asshown in previous works (Brinchmann et al. 2004; Tremonti et al.2004). This bias needs to be kept in mind when considering thediagrams and analysis in this work.Figure 2 also reveals the limitation of low-resolution spec-troscopy in finding all emission line sources, and thus the limita-tion of applicability of the method we explore here. Approximately5% of the SN(H α ) sample, and even 0.7% of the SN(H α ,H β ) sam-ple, actually have EW(H α ) less than zero (i.e. the emission line islost in the stellar absorption feature). These sources would never bepicked up as emission line galaxies in low-resolution spectra, andthe use of an emission-line equivalent width Balmer decrement todetermine the attenuation would return spurious results.Note that we have not included any cuts on redshift or thetype of emission-line galaxy as in previous works on SDSS emis-sion line galaxies (e.g. Kewley et al. 2006). Such redshift cuts arenecessary to make certain that aperture e ff ects do not play a part no r m a li z e d f r e q uenc y o f g a l a x i e s [Å] Figure 2.
Distribution of the H α emission line equivalent widths for thesamples considered in this work. All four histograms are normalized to theirpeak value, with the total number of galaxies in each sample listed in thekey in the upper left. The solid histogram shows all emission line galaxiesin SDSS DR7 (defined by the presence of H α in emission), and the threedashed curves show the distributions of samples defined by S / N cuts in theBalmer lines (as labelled in the upper left) considered in this work. in the derived galaxy properties (by sampling only a small, biasedpart of the galaxy, as discussed in Kewley et al. 2005) and to pre-vent luminosity biases at the higher redshifts. Yet as we care onlyfor the derived Balmer emission line fluxes and stellar equivalentwidths these issues do not strongly a ff ect our findings.Separating emission-line galaxies by class (i.e. star-forming orActive Galactic Nucleus dominated) is necessary when examiningthe structure of the forbidden emission lines (e.g. [O iii ] λ ff mann et al. 2003a,b). However, as discussed in the previ-ous section, the relative strength of the Balmer lines depend onlyweakly on local conditions, and will vary little in their intrin-sic ratios between being photoionized by AGN or by OB stars(i.e. H α / H β should be ∼ .
86 in star-forming galaxies and ∼ . ff erenceis significant and will have some bearing on the work in this pa-per, it is secondary to the e ff ects of dust attenuation. Only whencollisional heating dominates the atomic gas and the excitation ofhydrogen, such as in shocks or clouds in hot gas, can the intrinsicratios be significantly di ff erent (see e.g. Ferland et al. 2009), butthese processes are not expected to dominate most galaxies withinour sample. An additional reason to include AGN is that, in accor-dance with our main aim, separating out the contribution of AGNfrom lower S / N samples may prove problematic as the weak diag-nostic lines become lost within the noise.Approximately 2% of the full SDSS sample considered hereare duplicate observations of galaxies (i.e. ∼
4% of the sample arepairs). We have not removed these from the sample so as to includethe intrinsic scatter due to observational uncertainties in the subse-quent analysis.
The issue of simply using directly the equivalent widths ofthe Balmer lines as proxies for the line fluxes when calcu- he Balmer decrement of SDSS galaxies a) E( B-V ) b) [ Å ] E( B-V ) Figure 3.
The variation of the equivalent width based Balmer decrement(log[EW(H α ) / EW(H β )]) versus the stellar continuum-subtracted flux basedBalmer decrement for the SDSS SN(H α ,H β ) sample. All axes are normal-ized by the intrinsic Balmer ratio, (H α/ H β ) I = .
86. In the left diagram,the EW(H α / H β ) has not been corrected for the di ff erence in continuum fluxat the H α and H β wavelengths (F λ (H α ) / F λ (H β )), while in the right this isincluded. The upper left hand corner shows the median uncertainties for thesample, and the straight line indicates a 1:1 relation. The colours and asso-ciated colourbars indicate the median H δ Abs and log[EW(H α )] respectivelyin each pixel. The top axes give the resulting E( B − V ) from the balmerdecrement assuming the O’Donnell (1994) Galactic extinction curve. lating the Balmer decrement can be seen in figure 3 whichshows the spread of the equivalent width based Balmer decre-ment (log[EW(H α ) / EW(H β )]) against the “true” Balmer decre-ment determined from the stellar continuum-subtracted line fluxes(log(H α / H β )) for the SN(H α ,H β ) sample. Both the EW Balmerdecrement and the flux Balmer decrement have been normalisedto the intrinsic ratio of 2.86, appropriate for a low density gas of T = K.One of the first obvious issues to be corrected for is the vari-ation of the underlying stellar continuum between the H α andH β wavelengths. In the left diagram of figure 3, we show thedistribution of log[EW(H α ) / EW(H β )], uncorrected for the contin-uum flux variation, while on the right the more accurate formof the EW Balmer decrement is used: log[EW(H α ) / EW(H β )] + log[F λ (H α ) / F λ (H β )], where F λ (H α ) is the continuum flux at H α ,determined from a 200 pixel median smoothing of the emission-line subtracted continuum.When uncorrected for the underlying continuum variationthere is a clear systematic o ff set of the EW Balmer decrement fromthe 1:1 relation of ∼ . ff set, yet a significant spread remains. This spread isdue to the e ff ect of the stellar Balmer absorption features. Withoutthese, EW(H α ) × F λ (H α ) should be, by definition, the flux of theline. The colors in figure 3a indicate the median H δ absorption in-dex (H δ Abs , Worthey & Ottaviani 1997; Kau ff mann et al. 2003a) ofthe sample in each pixel. As the figure shows, while the absolutestrength of the stellar Balmer absorption features does play a partin the observed o ff set of the SDSS galaxies’ EW Balmer decre-ments, the dominant mechanism for the o ff set and spread is the relative strength of the stellar absorption features to the emissionlines. This can be seen by the distribution of the equivalent widthof the H α emission line indicated by the colours in figure 3b, wherethere is a clear gradient of decreasing EW(H α ) with increasing o ff -set from the line. As the emission lines become weaker overall, thestellar absorption features, which are <
10Å as discussed in section2, obscure a greater fraction of H β relative to H α and therefore leadto a larger o ff set.As discussed in the introduction, the best way to compensatefor the e ff ect of the stellar absorption features on the emission lines a)c) b)d) Figure 4.
2D histograms of the distribution of the SDSS SN(H α ,H β )sample galaxies’ equivalent-width based Balmer decrements(log[EW(H α ) / EW(H β )]), including a constant correction for stellarBalmer absorption, versus the stellar continuum-subtracted flux basedBalmer decrements. Each figure shows a di ff erent bin of H α equivalentwidth, as labelled in lower right of each plot (in Å). As in figure 3, both axesare normalized by the intrinsic Balmer ratio, (H α/ H β ) I = .
86. The coloursindicate the log of the number density in each pixel, as labelled by thecolour bar on the right, with pixels with less than 5 galaxies excluded. Theerror bars in the upper left indicate the median uncertainty for each sample,with the total number of galaxies listed in the lower right of each plot. Notethat the y -axis has a di ff erent correction for stellar Balmer absorption, R ,for each plot as indicated in the lower left of each plot, and that galaxieswith H β still in absorption after correction (i.e. EW(H β ) + R <
0) have beenexcluded from the sample. is to fit the stellar continuum as done within the MPA / JHU SDSSdatabase. However, when only poor quality spectra are availablesuch as for high redshift galaxies, the determination of the Balmerabsorption features may be unreliable. One possible approach whenfaced with low resolution spectra is to assume that the absorptionequivalent width is constant for both Balmer lines across the wholesample. While figure 1 clearly shows that the absorption EW is not the same for all the Balmer lines, it provides a first step when infor-mation is sparse and uncertainties large. When a constant Balmerabsorption correction R is assumed for both EW(H α ) and EW(H β ),a correction factor of R =
4Å is determined when the o ff set of theSDSS galaxies’ EW Balmer decrements to the measured H α / H β ratios is minimized using an error-based weighting. The inclusionof this simple correction factor improves the situation when com-pared to that shown in figure 3, but with a still significant scatterof σ ∼ . ff set (i.e. Balmer absorption)for the whole sample. The value determined is biased towards highEW(H α ) galaxies, as these galaxies both dominate the sample andhave lower uncertainties, as discussed in section 3.When split into bins of di ff erent EW(H α ), more accurate fitswith di ff ering correction factors are obtained. In figure 4, we showthe fits for the galaxies split into four bins; 0 . < log(EW(H α )) < .
0, 1 . < log(EW(H α )) < .
5, 1 . < log(EW(H α )) < .
0, and2 . < log(EW(H α )) < .
5. The number of galaxies in each bin islisted in the lower right of each figure, and the median uncertaintiesare shown by the error bars in the upper left. Note that galaxies withH β still in absorption after the correction factor R is applied havebeen excluded, but that this is less than 0 .
2% of the sample in each
B. Groves, J. Brinchmann, & C.J. Walcher bin. As can be seen in the figure, the median uncertainties increasequickly with decreasing emission line equivalent width. It is forthis reason that galaxies with log(EW(H α )) < . y -axis for all four plots includes a correction for stellar ab-sorption; log([EW(H α ) + R ] / [EW(H β ) + R ]) + log[F λ (H α ) / F λ (H β )].As for the full sample, we determine the correction factor, R , foreach binned sample by finding the value that leads to the minimumo ff set from the 1:1 relation with the uncertainties giving 1 σ o ff -sets from this relation. The values determined are R = .
1, 3 . .
1, and 4 .
1Å for each increasing bin of EW respectively, as indi-cated in the lower-left of each plot in figure 4. The 1 σ uncertaintyaround R for each bin is approximately 1.0 (slightly less for theEW(H α ) > R is slightly skewed to highervalues, arising from the o ff set visible in 4a, discussed below. TheBalmer decrement determined from the EWs is significantly betterthan for the full sample, and especially so when no correction isincluded (figure 3), with dispersions of 1 σ ∼ α ) (figure 4a) sample appears by eye to beslightly o ff set form the line. A reasonable hypothesis is that thiso ff set arises due to our simple assumption of a constant correction R to both EW(H α ) and EW(H β ), whereas it is clear from 1 that theabsorption EW(H α ) is typically less than the absorption EW of H β by approximately a factor of 0.6 on average. However, changingthe correction factor of EW(H α ) to 0 . R and redoing the fit doesnot remove this o ff set. On closer examination it is clear that thiso ff set is due to a biasing of the fit to the high signal-to-noise data,which predominantly occur at high values of the H α / H β ratio due tomeasurement biases (i.e. there is a clear gradient in EW(H α ) fromtop to bottom in figure 4a). Assuming uniform weighting for thefit (i.e. ignoring the errors in EWs) gives a value of R = .
0, wellwithin the large uncertainties for R . For the other figures, assumingan o ff set correction factor for EW(H α ) of 0 . R , results in R = . .
7, and 3 .
7Å in terms of increasing EWs, with similar dispersionaround the relations. The results are within the uncertainties for R when assuming a constant correction, but in all cases indicate thenecessity for the correction of stellar absorption to the emissionlines of a factor of ∼ . < log(EW(H α )) < .
0, 1 . < log(EW(H α )) < .
5, and 2 . < log(EW(H α )) < . α and H β lines, with the median scatter in each pixel increasing sig-nificantly the further from the line. Thus the median uncertainty forthe outliers is greater than the median uncertainty of the sample asa whole in figure 4c.While figure 4 demonstrates that it is possible to determine theBalmer decrement to some accuracy from emission line equivalentwidths, the determination of the correction is dependent upon themeasurement of three quantities; EW(H α ), EW(H β ), and the fluxratio, F λ (H α ) / F λ (H β ). While the former two will be observable instrong emission line galaxies at high redshift, the flux ratio mayprove problematic to measure from spectra. However this ratio isclosely tied with the observed optical colours of the galaxy. In fig-ure 5 we show the distribution of the continuum fluxes measured atthe H α and H β wavelengths (F λ (H α ) / F λ (H β )) against the restframe g − r colour as measured from the SDSS fibre spectrum within the Figure 5.
Distribution of the full SN(H α ,H β ) SDSS sample ratio of con-tinuum fluxes measured at the H α and H β wavelengths (F λ (H α ) / F λ (H β ))against the restframe g − r colour as measured from the SDSS fibre spectrum.The solid line with diamonds shows the median F λ (H α ) / F λ (H β ), while thedashed lines show the 1 σ dispersion. Median uncertainties are indicated bythe error bars in the upper left. The thick dot-dot-dashed line indicates thebest fit linear relation, with y = − . + . g − r ) . full SN(H α ,H β ) sample. A linear fit to the correlation in this figurereturns log (F λ (H α ) / F λ (H β )) = − . + . g − r ) spec , (1)with a standard deviation of σ ∼ .
015 dex around this relation. Weuse the rest-frame g − r colour as a proxy for stellar continuum, butother colours such as r − i provide similar constraints. In the case oflow-S / N spectra, the rest-frame colour could be from SED fittingto broad-band magnitudes.Thus, in summary, the Balmer decrement for a low-resolution,strong-emission-line spectrum can be measured from the emissionline equivalent widths and colours alone with;log(H α/ H β ) = log EW(H α ) + . β ) + . ! + ( − . + . g − r ) rest ) , (2)with a scatter around this of σ ∼ .
05 dex, or ∼ . A V , assuming a Galactic extinction law (e.g. O’Donnell 1994). Forweaker emission line galaxies ((i.e. EW(H α ) < ff set( R ∼ .
5) should be used, as shown in figure 4. However, given thelarger uncertainties and greater dispersion seen at lower EW(H α ),a correction factor of R ∼ ∼ . A V ) and an extension to lower values(i.e EW Balmer decrement underestimate) due to low EW systems.One final note on this relation: as seen in figure 3, there is astrong bias in the sample of Balmer decrement with other galaxyproperties, as discussed in detail in several other SDSS papers (seee.g. Kau ff mann et al. 2003a; Garn & Best 2010). Thus, the relationshown above includes a combination of both galaxy type as wellas variation in extinction. The only way to remove fully this e ff ectis to match pairs of galaxies in as many property types excludingextinction, such as done in Wild et al. (2011b). Unfortunately whenapplied to the sample here, it was found that the range in extinctionwas not large enough to properly determine the relation. However,even given these uncertainties, this relation should still hold at sev-eral redshifts as high attenuations are on average associated withhigh gas masses, and thus high star formation rates and similar un-derlying continua at all redshifts. he Balmer decrement of SDSS galaxies Figure 6.
The distribution of H γ / H β ratios versus H α / H β ratios for theSDSS SN(H α ,H β ,H γ ) sample, with the number density of each pixel in-dicated by the bar on the right and pixels with less than 10 galaxies notshown. Both axes are normalised to their respective Case B ratios with(H α/ H β ) I = .
86 and (H γ/ H β ) I = . ff erent attenuation laws; Charlot & Fall (2000,CF00, diamonds), O’Donnell (1994, O’D94, triangles), andCalzetti et al.(2000, Cal00, plus signs) (see text). Each symbol represents a step of 0.5 in A V , up to A V = Inset : A zoomed in version of the figure, showing the po-sition of the zero point when the intrinsic ratios ((H α/ H β ) I and (H γ/ H β ) I )are taken to be at T = One issue with the previous section is that we assume throughoutthat the stellar-continuum subtracted emission line fluxes within theMPA / JHU database are correct. While the overall fits to the stellarcontinuum are impressively good with a median χ = .
01 per pixelacross the sample, there are appear to be remaining issues aroundthe Balmer lines. In the following we concentrate on the SDSS DR7Balmer emission-line fluxes corrected for the underlying stellar ab-sorption features from the MPA / JHU database, and explore theiruncertainties using the known intrinsic values and commonly usedattenuation and extinction laws. β When considered alone, the ratio of H α / H β cannot indicate prob-lems with the measurement of the lines involved unless it is signif-icantly below the expected value of the unattenuated ratio. This isbecause the larger values of the emission line ratio can be caused byattenuation by intervening dust, with the intrinsic ratio dependentthe emitting gas density and temperature (as discussed in section2). However by examining several of the Balmer lines at once thesedependencies can be accounted for.Figure 6 shows the variation of the H γ / H β ratio against theH α / H β ratio for the SN(H α ,H β ,H γ ) SDSS sample. Both ratios havebeen normalized to their Case B, T = n e =
100 cm − in-trinsic ratios ((H α/ H β ) I = .
86, (H γ/ H β ) I = . ff set of the sample from the zero point,indicating most SDSS galaxies undergo some attenuation (as seen in the previous plots), with the correlation between the two ratiosas expected from the reddening laws applied to the intrinsic ratio.The three di ff erent lines overplotted show the e ff ect of threedi ff erent attenuation laws commonly assumed in the analysis ofgalaxies. For all three lines, the symbols indicates steps of 0.5 in A V , up to A V = ff er attenuation due to the mixtureof emitting sources and absorbing medium. However, as discussedin Kennicutt et al. (2009) and can be seen in figure 6, the use ofa foreground dust screen with galactic extinction is indistinguish-able from the other laws, especially given the uncertainty withinthe SDSS sample. We assume a total to selective V -band extinctionof R V = .
1, the average value in our galaxy.The Calzetti et al. (2000) attenuation law (Cal00) was ob-tained from the continuum and Balmer decrement of local activelystar-forming galaxies, thus matching the high EW(H α ) galaxies inthe sample. Note that as only ratios are analysed here, the di ff er-ence between the colour excess ( E ( B − V )) of the stellar continuumand nebular lines noted by Calzetti et al. is e ff ectively scaled out.The R V used here is 4.05, as given by Calzetti et al. (2000) from thecomparison of the observed infrared flux to that predicted from theobscuration of the optical-ultraviolet light.The Charlot & Fall (2000) attenuation law (CF00) is a moresimple, empirical law put forward to allow for the di ff erent colourexcesses and attenuations observed by Calzetti et al. (2000) be-tween the nebular emission lines and stellar continuum. It breaksthe attenuation into two components; the ‘di ff use ISM’ componentthat describes the e ff ective obscuration of all stars in a galaxy bythe di ff use dust, and the ‘birth cloud’ component that describes theadditional extinction su ff ered by the H ii regions from which thenebular emission lines arise, giving A λ A V = µ ( λ/λ V ) − . + (1 − µ )( λ/λ V ) − . , (3)where λ V = − . ff use ISM wasempirically derived by Charlot & Fall (2000) with a comparisonof nearby galaxies, while the − . µ indicates the fraction of the attenuation su ff ered by thenebular lines by each component. We assume µ = . ff erent attenuation laws, and pro-vide an answer on which law is best (or least bad) to apply to anensemble of galaxies. Such work has been done before for com-paring galactic extinction laws using planetary nebulae (Phillips2007). Note that the di ff erent R V between the Cal00 and O’D94laws is what causes the di ff erence in expected H α / H β for the same A V , while the CF00 and Cal00 have similar A V as determined fromH α / H β , but not from H γ / H β . Two, that the scatter of the SDSSgalaxies is large around the three laws, preventing this possibility,though this scatter is not significant when compared to the medianuncertainty as shown by the error bars. Third, and most importantly,while the slope of SDSS galaxies matches that given by the atten-uation laws, there is a systematic o ff set of the SDSS galaxies whencompared to all three attenuation laws . This o ff set is significant,and cannot be explained by assuming more extreme (and therefore B. Groves, J. Brinchmann, & C.J. Walcher
Figure 7.
The same plot as figure 6, except using the SDSS DR4 MPA / JHUcatalogue. The same SN cuts on H α , H β , and H γ are applied, with ∼ less likely) attenuation laws or by assuming large values of R V , asthe zero point itself appears to be o ff set.Neither can this situation be remedied by assuming di ff erentvalues for the unattenuated Balmer ratios. As discussed in section 2,the intrinsic Balmer emission-line ratios are sensitive to the temper-ature of the ionized gas from which they arise, and, more weakly,to the density of the gas as well The inset in figure 6 shows a closeup of the zero point of figure 6, i.e. galaxies with little or no at-tenuation. Over this are plotted 3 symbols indicating the positionwhere the zero point would be for 3 di ff erent average H ii regiontemperatures; 5,000K, 10,000K (assumed within the figure), and20,000K. All assume Case B ratios, and a typical H ii gas densityof n e = cm − . These 3 temperatures encompass the range oftemperatures expected, with typical solar metallicity H ii regionshaving T e ∼ ff ects ofattenuation and the observed o ff set, and that the variation in intrin-sic ratios is in the same sense as that due to the e ff ects of attenuation(as shown by the Calzetti et al. (2000) law), thus the intrinsic ratiocannot be the cause of the o ff set.A possible cause for this o ff set can be found when theMPA / JHU DR4 catalogue is examined instead. Using the same SNcuts on H α , H β , and H γ , figure 7 shows the same plot as figure 6for the DR4 sample. In most ways this figure is exactly the same(as it should be), except in two respects: the DR4 SN(H α ,H β ,H γ )sample only has ∼ ∼ ff set with respect to the attenuation laws seen in figure 6.As mentioned in section 3, the major di ff erence between theDR4 and DR7 line fluxes from the MPA / JHU catalogues is the ver-sion of the GALAXEV models used for the continuum fits. In somerespects the di ff erence seen in the figures is surprising, as the me-dian χ of the fits to the continuum in DR7 is reduced compared tothe DR4 fits, from χ = . χ = β line region, as ano ff set in the H β line flux would also explain the increasing o ff -set at higher (H α / H β ) between the SDSS galaxies and the atten-uation laws, and this region has been observed to be mismatchedbetween models and the spectra of some globular clusters (see e.g. Figure 8. a)
The same diagram as Figure 6, but rotated to A V axes using theattenuation law of Calzetti et al. (2000). The x -axis is the A V as measuredfrom the (H α / H β ) ratio, while the y -axis is the o ff set from the expected(H γ / H β ) ratio based on this A V . b) The same as a), but the H β line flux hasbeen corrected for under subtraction of the stellar continuum by 0.35Å. Walcher et al. 2009; Poole et al. 2010). This di ff erence in slope ismore clearly seen in figure 8a where we have rotated and scaledfigure 6 to the A V plane using the attenuation law of Calzetti et al.(2000), where the o ff set from the x -axis is more clearly seen. Simi-lar results are seen if another attenuation law is used. In this frame,the y -axis is the o ff set from the expected (H γ / H β ) ratio based onthe A V as determined by the (H α / H β ) ratio.By “correcting” for the incorrectly subtracted stellar H β equiv-alent width we can fix figure 8a. This is what we have done in fig-ure 8b, where we have added 0.35Å to the emission line equivalentwidth (i.e. “True” H β = H β + λ (H β )). The correction of 0.35Åwas determined by minimizing the o ff set from the Calzetti law (thisvalue depends only weakly on the choice of attenuation law). Thismeans that the stellar absorption equivalent width of H β is system-atically underestimated by 0.35Å in the CB08 continuum fits toDR7 SDSS spectra.The fact that this 0.35Å underestimation is systematic is in-teresting, as we would expect that any error would depend on thestrength of the Balmer features, either measured through the H δ Abs or the emission line equivalent widths, both of which do correlatewith H α / H β as seen in figure 3 , yet no correlation is observed.What the underlying cause of this systematic underestimation isunknown, yet it must be taken into consideration when determin- he Balmer decrement of SDSS galaxies ing the A V from the Balmer decrement in the SDSS DR7 MPA / JHUcatalogue. It is possible that this issue arises due to the misclas-sification of the spectral resolution of the MILES library (as dis-cussed in Falc´on-Barroso et al. 2011) in the implementation in theCB08 code, but this issue is now known and currently under in-vestigation. This investigation goes beyond the scope of the workpresented here but we note that the models used here are earlyversions of the CB08 library and these issues are expected to besolved within the to-be-published models. When the new A V is cal-culated from the H α / H β ratio including the systematic 0.35Å o ff set(using e.g. Calzetti et al. 2000, law), a mean di ff erence of − A V estimates, increas-ing slightly at higher A V . This suggests that previous DR7 A V es-timates, such as in Garn & Best (2010), are overestimated by thisvalue.Similarly this 0.35Å correction must be included in our EWBalmer decrement (equation 2) leading to a new equation,log(H α/ H β ) = log EW(H α ) + . β ) + . ! + ( − . + . g − r ) rest ) , (4)which more closely matches our expectations of di ff erent stellar ab-sorption equivalent widths between H α and H β . For weaker emis-sion line galaxies, the o ff set would be smaller than 4.1, as shown infigure 4 and discussed at the end of section 4. δ While examining the issue in H β , a similar issue was found for H δ that we present here as a curiosity. When H δ / H α versus H γ / H α isplotted, using the SN(H α ,H β ,H γ ,H δ ) sample of SDSS galaxies andavoiding the problematic H β line, the tight correlation betweenthese two ratios, matching closely that expected from the attenu-ation by dust. However, upon closer examination, a systematic o ff -set is observed between the galaxies and attenuation laws. As inthe previous subsection on H β , the o ff set is clearer when rotated tothe A V plane, which is what we show in figure 9, where the x -axisis the A V determined from H γ / H α using the Calzetti et al. (2000)law, with the y -axis the o ff set from this A V when determined fromthe H δ / H α ratio. The median o ff set is ∼ − .
05 for most of the A V range shown here, meaning that the A V determined from H δ / H α islower than that determined from H γ / H α . The o ff set is seen for allattenuation laws considered here.More importantly, the o ff set is also observed in the DR4 sam-ple, though with greater uncertainty due to low number statistics.As with the H β line there appears to be no correlation of the o ff setwith emission line equivalent widths, or stellar age determinantslike H δ Abs or the D n ff mann et al. 2003a, fordefinitions of these indices). Neither does it appear to be correlatedwith H α / H β or other emission line or attenuation tracers. Thus, dueto the lack of di ff erence between DR4 and DR7, the strong EWbias of the sample (as shown in figure 2), and the fact that the un-certainty is dominated by the H δ line, it is still not known whatexactly causes this o ff set. It is most likely an issue due to the under-lying continuum, but an investigation into the stellar models goesbeyond the scope of this work. Thus we present this issue for nowas a curiosity and a cautionary note of the level of systematic un-certainties in determining weak line fluxes from the SDSS sample. Figure 9.
The distribution of H δ / H α versus H γ / H α for theSN(H α ,H β ,H γ ,H δ ) sample of SDSS DR7 galaxies ( ∼ A V plane as determinedfrom the Calzetti et al. (2000) law, indicated by the straight line. Thenumber of galaxies in each pixel is indicated by colours (as labelled), withpixels with less than 5 galaxies not shown. We have examined the possibility of using equivalent widths ofthe Balmer emission lines to determine the Balmer decrement, andhence attenuation, of a galaxy. Using the Sloan Digital Sky Sur-vey we were able to determine a statistically representative relationbetween the continuum-subtracted Balmer emission line flux ra-tio and the equivalent widths (EW) of the Balmer emission-linescombined with a rest-frame colour, correcting for the e ff ects of thestellar absorption features:log(H α/ H β ) = log EW(H α ) + . β ) + . ! + ( − . + . g − r )) , (5)for galaxies with EW(H α ) > ∼ σ ∼ .
06 dex,or 0.4 mag in A V , indicating the possible variation for individualobjects. For galaxies with EW(H α ) <
30Å smaller correction fac-tors (3.5 for EW(H α ), 3.8 for EW(H β )) should be used. However,given the scatter at low EW values, the equation above can be usedabove for all galaxies allowing for a much greater uncertainty inthe final Balmer ratio or A V determined.In addition, by comparing the Balmer decrement (H α / H β versus H γ / H β ) we discovered that the H β emission line equiva-lent width (and hence flux) is underestimated by 0 .
35Å in theJHU / MPA DR7 SDSS database, due to an issue in the H β regionof the 2008 version of the Charlot & Bruzual stellar populationsynthesis code GALEXEV. This leads to an overestimation of theattenuation of the SDSS galaxies of 0.07 magnitudes in A V assum-ing a Calzetti et al. (2000) attenuation law.Finally, we also discovered a strange o ff set in the H δ emis-sion line fluxes observable in both the DR4 and DR7 releases ofthe MPA / JHU database which we present both as a curiosity and asa warning on the underlying issues in interpreting weak-line emis-sion lines in a statistical sample B. Groves, J. Brinchmann, & C.J. Walcher
ACKNOWLEDGEMENTS
BG would like to thank V. Wild for providing her PCA principalcomponent values available and very helpful discussions, and theauthors would like to thank the referee for helpful comments.Funding for the SDSS and SDSS-II has been provided bythe Alfred P. Sloan Foundation, the Participating Institutions, theNational Science Foundation, the U.S. Department of Energy,the National Aeronautics and Space Administration, the JapaneseMonbukagakusho, the Max Planck Society, and the Higher Ed-ucation Funding Council for England. The SDSS Web Site is .The SDSS is managed by the Astrophysical Research Con-sortium for the Participating Institutions. The Participating Institu-tions are the American Museum of Natural History, AstrophysicalInstitute Potsdam, University of Basel, University of Cambridge,Case Western Reserve University, University of Chicago, DrexelUniversity, Fermilab, the Institute for Advanced Study, the JapanParticipation Group, Johns Hopkins University, the Joint Institutefor Nuclear Astrophysics, the Kavli Institute for Particle Astro-physics and Cosmology, the Korean Scientist Group, the ChineseAcademy of Sciences (LAMOST), Los Alamos National Labora-tory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State Uni-versity, Ohio State University, University of Pittsburgh, Universityof Portsmouth, Princeton University, the United States Naval Ob-servatory, and the University of Washington.
REFERENCES
Abazajian, K. N., et al. 2009, ApJS, 182, 543Adelman-McCarthy, J. K., et al. 2006, ApJS, 162, 38Baker, J. G., & Menzel, D. H. 1938, ApJ, 88, 52Berman, L. 1936, MNRAS, 96, 890Brinchmann, J., Charlot, S., White, S. D. M., Tremonti, C., Kau ff -mann, G., Heckman, T., & Brinkmann, J. 2004, MNRAS, 351,1151Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000Calzetti, D., Armus, L., Bohlin, R. C., Kinney, A. L., Koornneef,J., & Storchi-Bergmann, T. 2000, ApJ, 533, 682Calzetti, D. 2001, PASP, 113, 1449Cappellari, M., & Emsellem, E. 2004, PASP, 116, 138Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345,245Cenarro, A. J., et al. 2007, MNRAS, 374, 664Charlot, S., & Fall, S. M. 2000, ApJ, 539, 718Cid Fernandes, R., Mateus, A., Sodr´e, L., Stasi´nska, G., & Gomes,J. M. 2005, MNRAS, 358, 363da Cunha, E., Eminian, C., Charlot, S., & Blaizot, J. 2010, MN-RAS, 403, 1894Dopita, M. A., & Sutherland, R. S. 2003, Astrophysics of the dif-fuse universe, Berlin, New York: Springer, 2003. Astronomy andastrophysics library, ISBN 3540433627Falc´on-Barroso, J., S´anchez-Bl´azquez, P., Vazdekis, A., Riccia-rdelli, E., Cardiel, N., Cenarro, A. J., Gorgas, J., & Peletier, R. F.2011, A&A, 532, A95Ferland, G. J. 1999, PASP, 111, 1524Ferland, G. J., Fabian, A. C., Hatch, N. A., Johnstone, R. M.,Porter, R. L., van Hoof, P. A. M., & Williams, R. J. R. 2009,MNRAS, 392, 1475Ferland, G. J., Korista, K. T., Verner, D. A., Ferguson, J. W., King-don, J. B., & Verner, E. M. 1998, PASP, 110, 761 Gallazzi, A., Charlot, S., Brinchmann, J., White, S. D. M., &Tremonti, C. A. 2005, MNRAS, 362, 41Garn, T., & Best, P. 2010, arXiv:1007.1145Groves, B. A., Dopita, M. A., & Sutherland, R. S. 2004, ApJS,153, 9Gonz´alez Delgado, R. M., & Leitherer, C. 1999, ApJS, 125, 479Gonz´alez Delgado, R. M., Leitherer, C., & Heckman, T. M. 1999,ApJS, 125, 489Kau ff mann, G., et al. 2003, MNRAS, 341, 33Kau ff mann, G., et al. 2003, MNRAS, 346, 1055Kennicutt, R. C., Jr., et al. 2009, ApJ, 703, 1672Kewley, L. J., Jansen, R. A., & Geller, M. J. 2005, PASP, 117, 227Kewley, L. J., Groves, B., Kau ff mann, G., & Heckman, T. 2006,MNRAS, 372, 961Lamareille, F., Contini, T., Le Borgne, J.-F., Brinchmann, J., Char-lot, S., & Richard, J. 2006, A&A, 448, 893Le Borgne, J.-F., et al. 2003, A&A, 402, 433Liang, Y. C., Hammer, F., Flores, H., Gruel, N., & Ass´emat, F.2004, A&A, 417, 905Luridiana, V., Sim´on-D´ıaz, S., Cervi˜no, M., Gonz´alez Delgado,R. M., Porter, R. L., & Ferland, G. J. 2009, ApJ, 691, 1712Menzel, D. H., & Baker, J. G. 1937, ApJ, 86, 70Ocvirk, P., Pichon, C., Lanc¸on, A., & Thi´ebaut, E. 2006, MNRAS,365, 74O’Donnell, J. E. 1994, ApJ, 422, 158Osterbrock, D. E., & Ferland, G. J. 2006, Astrophysics of gaseousnebulae and active galactic nuclei, 2nd. ed. by D.E. Osterbrockand G.J. Ferland. Sausalito, CA: University Science Books, 2006Phillips, J. P. 2007, New A, 12, 378Poole, V., Worthey, G., Lee, H.-c., & Serven, J. 2010, AJ, 139,809S´anchez-Bl´azquez, P., et al. 2006, MNRAS, 371, 703Seaton, M. J. 1959, MNRAS, 119, 90Storey, P. J., & Hummer, D. G. 1995, MNRAS, 272, 41Tojeiro, R., Heavens, A. F., Jimenez, R., & Panter, B. 2007, MN-RAS, 381, 1252Tremonti, C. A., et al. 2004, ApJ, 613, 898Walcher, C. J., Coelho, P., Gallazzi, A., & Charlot, S. 2009, MN-RAS, 398, L44Wild, V., Kau ffff