Quantifying the poor purity and completeness of morphological samples selected by galaxy colour

ABSTRACT

1 INTRODUCTION

One of the central observations to be explained by any model of the galaxy population is that the dynamical histories and the star formation histories of galaxies correlate well. Dynamical histories are imperfectly traced by galaxy morphology, and star formation histories by integrated colours. The observation of a correlation between colour and morphology, alongside correlations of both properties with large-scale galactic environment, is among the central pieces of evidence of models of hierarchical galaxy evolution, where massive galaxies assemble over time through multiple minor mergers and occasional major mergers (e.g. as described in Steinmetz & Navarro 2002).

As astronomical surveys grew in size, obtaining visual morphology became more challenging. The idea of making morphological selections using colour as a proxy for morphology provided a convenient solution and became popular once large-scale, semi-automated imaging surveys [e.g. the Sloan Digital Sky Surveys (SDSS) Main Galaxy Sample (MGS); Strauss et al. 2002] quantified the correlation between colour and morphology. Although it had been noted for decades before that spiral galaxies tend to be bluer than elliptical galaxies (e.g. Zwicky 1955 comments that this had been ‘known for a long time’), such large surveys confirmed the existence of the blue cloud dominated by disc galaxies and the red sequence dominated by elliptical galaxies (Baldry et al. 2004, 2006; Willmer et al. 2006; Ball, Loveday & Brunner 2008; Brammer et al. 2009).

Many studies have since gone on to reveal the presence of significant fractions of spirals in the red sequence (∼30 per cent) and/or smaller numbers of blue ellipticals (up to ∼10 per cent; see e.g. van den Bergh 1976; Bamford et al. 2009; Schawinski et al. 2009; Skibba et al. 2009; Wolf et al. 2009; Bundy et al. 2010; Masters et al. 2010b; Rowlands et al. 2012; Bonne et al. 2015; Fraser-McKelvie et al. 2016; Mahajan et al. 2020; Tuttle & Tonnesen 2020; Xu et al. 2021). Despite this, there remains a persistent idea in the literature that there are colour thresholds that can be used to make a clean morphological sample.

The publication of ‘Color Separation of Galaxy Types in the Sloan Digital Sky Survey Imaging Data’ (Strateva et al. 2001) may perhaps be credited in large part to the common use of colour to separate samples by morphology. Strateva et al. used SDSS photometry of almost 150 000 galaxies, finding a strong bimodality in u − r colours, and used the morphologies of 267 galaxies in that sample to make the claim that red galaxies ‘roughly correspond’ to early-types (which they define as Sa, S0, and ellipticals), while blue galaxies correspond to the late-types (defined as Sb and Sc).

The impact of this conclusion can be traced via the citation trail through the literature. For example, Bell et al. (2004) state that the definition of an early-type should be redefined in terms of colour due to the results of Strateva et al. (2001), Hogg et al. (2002), and Blanton et al. (2003). Similarly, following on from the work of Strateva et al., Park & Choi (2005) claim that a cut in a two-dimensional colour–colour parameter space is accurate enough to replace visual morphological classification. In addition, Faber et al. (2007, using Strateva et al. 2001 as the primary reference) state that ‘early-type E/S0s populate a narrow red sequence that is separated from bluer, star-forming spirals by a shallow valley’, going on to say ‘not only does colour sort galaxies cleanly into bins, it is also highly relevant to the emergence of the Hubble sequence’.

This practice of equating colour and morphology is not limited to optical photometry. For example, Wright et al. (2010) and Jarrett et al. (2017) both label regions on a Wide-field Infrared Survey Explorer (WISE) far-infrared (FIR) colour–colour plot by a mix of morphology and emission properties [e.g. labels include ‘spirals’, but also low-ionization nuclear emission-line regions (LINERs)]. Similarly, spectra or spectral energy distributions (SEDs) are also sometimes labelled by morphology, for example Benítez et al. (2004) label their SED collections by morphology.

It also remains a common practice, particularly in studies that use galaxies as tracers of the large-scale structure of the Universe, to implicitly assume that blue colours indicate disc structure (or late-type) and red colours indicate ellipticals (or early-type; e.g. Dawson et al. 2013 use red optical colours to select a sample of passively evolving early-type galaxies for use in the Baryon Oscillation Spectroscopic Survey of SDSS-III). This is equivalent to assuming that the star formation histories (as traced imperfectly by colours) and orbital motions (as traced imperfectly by morphology) of galaxies are uniquely connected [for a selection of further examples of this see e.g. Bell et al. 2004; Weinmann et al. 2006; van den Bosch et al. 2008; Chilingarian & Zolotukhin 2012 who claim that by moving to near-ultraviolet (NUV) bands, clean morphological cuts can be made]. For a more extended list of examples of publications that conflate colour and morphology in galaxy samples, see the Introduction of Masters et al. (2019).¹

The use of colour as a proxy for morphology certainly is reasonable as a first-order, low-redshift approximation. It is also considerably easier to automate colour measurements than visual morphologies in large extragalactic surveys. These two factors have likely strongly motivated the field’s widespread adoption of this practice. However, in this short paper we argue that the impurity and incompleteness this introduces into modern analyses of galaxy evolution is often significant, can lead to incomplete and/or biased conclusions, and is no longer technologically necessary. To demonstrate this, we make use of the Galaxy Zoo 2 (GZ2) morphologies (based on citizen science inspection of SDSS images) along with SDSS, Two Micron All Sky Survey (2MASS), and Galaxy Evolution Explorer (GALEX) photometry to quantify the purity and completeness of galaxy samples using colour as a proxy for morphology to split into ‘smooth’ (also known as early-types; this selection in GZ2 includes both elliptical and visually smooth S0 galaxies) or disc galaxies (GZ2 selected ‘featured or disc’ galaxies). We will quantify and explore the impurity and incompleteness involved in using a colour selection as a proxy for morphology selection and discuss the biases this assumption may introduce. We recommend that any study that uses colour to morphologically categorize galaxies should be cognizant of the limitations discussed.

We describe the data sources and sample selection in Section 2, and our method in Section 3. Our results are shown in Section 4, and we conclude in Section 5. In the rest of this work we adopt the Planck 2015 (Planck Collaboration XIII 2016) cosmological parameters with (Ω_m, Ω_λ, h) = (0.31, 0.69, 0.68), where distances are needed to create physical units.

2 DATA AND SAMPLE SELECTION

We used morphological classifications from GZ2 (Willett et al. 2013) that were initially selected from the SDSS MGS (Strauss et al. 2002), so have optical magnitudes available across u, g, r, i, and z wavebands. This parent sample will be referred to as the gz2sample and has 239 695 galaxies, corresponding to the brightest 25 per cent of the MGS (or m_r < 17 mag) from SDSS Data Release 7 (DR7; Abazajian et al. 2009) in the redshift range 0.01 < z < 0.24 (median z = 0.075). We cross-matched the gz2sample to the GALEX survey (Martin et al. 2005) to obtain NUV magnitudes for 126 315 galaxies matched with a search radius of 1 arcsec in right ascension and declination (see Smethurst et al. 2015). This will be referred to as the gz2galexsample (median z = 0.068). We also cross-matched the gz2sample to the 2MASS survey (Skrutskie et al. 2006) to obtain J, H, and K magnitudes for 99 101 galaxies. This will be referred to as the gz22masssample (median z = 0.077). Finally, we also cross-matched the gz2galexsample to the gz22masssample to give 99 065 galaxies having optical, ultraviolet (UV), and NIR photometry, in the gz2galex2masssample (median z = 0.070).

We used the SDSS Petrosian magnitudes, the GALEX automagnitudes, and 2MASS Extended Source Catalog (XSC) standard aperture (derived from the K_s-band 20 mag arcsec⁻² isophote, see section 3.4 of Jarrett et al. 2000) to determine colours (for a discussion of aperture bias between different surveys see Hill et al. 2011). All observed optical, UV, and NIR magnitudes are corrected for galactic extinction (Oh et al. 2011) by applying the Cardelli, Clayton & Mathis (1989) law (giving a typical correction of u − r ∼ 0.05). We also adopt k-corrections to z = 0.0 (following the method in Bamford et al. 2009).

GZ2 morphological classifications are described in detail in Willett et al. (2013) but we briefly summarize here. GZ2 is a citizen science project that crowd sourced classifications from the public online. An average of around 40 volunteers classified each galaxy, using a tree of questions. For this work we focus only on the first question in the tree: ‘Is the galaxy simply smooth and round with no sign of a disc?’ to which the volunteers could answer ‘Smooth’, ‘Features or disc’ or ‘Star/artefact’. Volunteer answers are aggregated into vote fractions after downweighting inconsistent answers. These vote fractions are then debiased to account for the impact of redshift on image quality. In this work, we use the vote fractions debiased using the method described in Hart et al. (2016) that provides an improved debiasing technique over that initially presented in Willett et al. (2013). Following this procedure we make use of the ‘debiased vote fractions’ for disc or featured galaxies (p_d) and smooth galaxies (p_s) to morphologically classify the galaxies in our samples.

We use a conservative cut to select a very pure sample of featured galaxies (most of which are spiral discs) as those with GZ2 debiased vote fractions of p_d > 0.8 and smooth galaxies (ellipticals and featureless S0s) as those with p_s > 0.8. Example SDSS images of those galaxies selected as discs and smooth are shown in Fig. 1. Intermediate galaxies are not included in our analysis (those with p_s ∼ p_d ∼ 0.5), which are a mixture of genuinely intermediate galaxies (i.e. those of lenticular or S0 morphologies) and galaxies where morphological classification was inconclusive (i.e. due to poor image resolution or higher redshift). We note that detection fractions differ by morphology in our different subsets. For example, using the conservative cuts described above, in the gz2sample, 43 per cent of galaxies are discs, and 22 per cent smooth; this is very similar in the gz22masssample, but changes to 41 per cent disc and just 8 per cent smooth galaxies in the gz2galexsample as smooth galaxies are more likely to be undetected in UV bands (Smethurst et al. 2015; Schombert 2016). For a comparison of GZ2 morphologies to other morphological classification works, such as the expert visual classification of Nair & Abraham (2010) or the automatic classification of Huertas-Company et al. (2011), see section 5 of Willett et al. (2013).

Figure 1.

SDSS gri postage stamp images showing five randomly chosen red discs (top row), blue discs (second row), red smooth (third row), and blue smooth galaxies (bottom row) in the redshift range 0.05 < z < 0.075, morphologically classified using Galaxy Zoo vote fractions (see Section 2). The white bar in the top left-hand panel shows the 5 arcsec pixel scale.

Open in new tabDownload slide

3 METHOD

In this work, we want to investigate the purity and completeness of a sample when using colour as a proxy for morphology. In the literature, this is often done by applying a threshold cut in a chosen colour (Bell et al. 2004; Weinmann et al. 2006; Faber et al. 2007; van den Bosch et al. 2008; Cooper et al. 2010; Ascasibar & Sánchez Almeida 2011; Zehavi et al. 2011) to classify galaxies as either early-type/smooth (those redder than the threshold) or late-type/discs/featured (those bluer than the threshold). However, such samples will be contaminated by red late-types and blue early-types. Therefore to study the purity and completeness of a sample of early-type galaxies selected in this way we need to define:

• true positive (TP)  = Galaxy Zoo smooth galaxies classified as early-type based on red colour (i.e. red early-types);

• false positive (FP)  = Galaxy Zoo featured/disc galaxies classified as early-types based on red colour (i.e. red spirals);

• false negative (FN)  = Galaxy Zoo smooth galaxies classified as late-type based on blue colour (i.e. blue early-types).

Similarly to select a sample of late-type (disc or featured) galaxies in this way:

• true positive (TP)  = Galaxy Zoo featured/disc galaxies classified as late-types based on blue colour (i.e. blue spirals);

• false positive (FP)  = Galaxy Zoo smooth galaxies classified as late-type based on blue colour (i.e. blue early-types);

• false negative (FN)  = Galaxy Zoo featured/disc galaxies classified as early-type based on red colour (i.e. red spirals).

We calculate both purity and completeness at 100 different colour values for all optical colour combinations in the gz2sample, all NUV–optical colour combinations in the gz2galexsample, all optical–infrared colour combinations in the gz22masssample, and all NUV–infrared colour combinations in the gz22masgalexsample. The values were chosen as 100 equally spaced intervals between the 1st and 99th percentile of each colour distribution. We then determine the colour at which a compromise between purity and completeness is achieved for all magnitude band combinations, i.e. the colour at which the purity and completeness are equal.

4 RESULTS AND DISCUSSION

We investigate the purity and completeness of using a single colour threshold to select a morphological sample for various colour combinations across the UV, optical, and infrared wavelength ranges of the GALEX, SDSS, and 2MASS. The colour threshold at which a compromise between purity and completeness is achieved (i.e. when they are equal) is listed in Table 1.

We find that NUV − r is the best colour to use to achieve an ideal compromise purity and completeness of |$65.8{{\ \rm per\ cent}}$| for a sample of smooth galaxies and |$92.8{{\ \rm per\ cent}}$| for disc galaxies, using a colour threshold of NUV − r = 4.961. If optical observations are not available, then NUV − J is the next best option with |$66.7{{\ \rm per\ cent}}$| purity/completeness for smooth galaxies and |$92.1{{\ \rm per\ cent}}$| purity/completeness for disc galaxies at a colour threshold of NUV − J = 7.091. If UV observations are not available, then u − J is the next best option with |$44.4{{\ \rm per\ cent}}$| purity/completeness for smooth galaxies and |$78.5{{\ \rm per\ cent}}$| purity/completeness for disc galaxies at a colour threshold of u − J = 4.290. If neither UV nor infrared observations are available, the next best option is g − r with |$56.6{{\ \rm per\ cent}}$| purity/completeness for smooth galaxies and |$76.0{{\ \rm per\ cent}}$| purity/completeness for disc galaxies at a colour threshold of g − r = 0.742 (similarly, u − r also achieves a purity/completeness of |$56.3{{\ \rm per\ cent}}$|/|$77.2{{\ \rm per\ cent}}$| at a colour threshold of u − r = 2.340). In Fig. 2, we show how the purity and completeness change with different colour thresholds for each of these five colours, demonstrating how our quoted thresholds in Table 1 result in a compromise between maximizing purity and completeness.

Figure 2.

The distribution of NUV − r (top), NUV − J (top middle), u − J (middle), g − r (bottom middle), and u − r (bottom) for galaxies classified as discs (blue histogram) and smooth (red histogram). The completeness (solid lines) and purity (dashed lines) are shown for selecting early-type (red lines) and late-types (blue lines) galaxy samples. These figures show how changing the colour threshold to morphologically classify galaxies based on their colour results in incomplete samples. The black dashed vertical line shows the colour threshold at which a compromise between purity and completeness is achieved (i.e. they are equal). If there is no other option but to use colour to make a morphological classification, then the purity and completeness are both maximized when a threshold of NUV − r = 4.96, NUV − J = 7.09, u − J = 4.55, g − r = 0.74, or u − r = 2.34 is employed.

Open in new tabDownload slide

The addition of NIR bands to optical bands does not significantly improve the compromise between purity and completeness achievable when only optical observations are available. However, it is clear from Table 1 that having rest-frame NUV magnitudes does significantly improve the compromise between purity and completeness when using colour to morphologically classify a sample, especially for constructing a disc galaxy sample. In this we agree with the findings of Chilingarian & Zolotukhin (2012) who suggest NUV − r is a significantly better choice than optical selection when dividing the galaxy population. They suggest a threshold of NUV − r > 4 to select early-types, as opposed to the NUV − r = 4.961 threshold we found in this study (see Table 1). Using the Chilingarian & Zolotukhin (2012) cut of NUV − r > 4 results in a sample of early-type galaxies with a purity of |$44.1{{\ \rm per\ cent}}$| and a completeness of |$76.8{{\ \rm per\ cent}}$|⁠, and a late-type sample with a purity |$94.5{{\ \rm per\ cent}}$| and a completeness of |$80.5{{\ \rm per\ cent}}$|⁠. Therefore |${\sim} 20{{\ \rm per\ cent}}$| of disc galaxies will be missed using the Chilingarian & Zolotukhin (2012) threshold, and these missing disc galaxies consist of ‘red spiral’ galaxies of particular interest for understanding quenching of star formation (Masters et al. 2010b; Cortese 2012; Tojeiro et al. 2013; Fraser-McKelvie et al. 2016, 2018; Mahajan et al. 2020).

However, as is clear from comparing the red-filled distributions across the panels of Fig. 2, a significant number of smooth galaxies are not detected in NUV bands. This reduces the ultimate sample size and the effectiveness of NUV colours at selecting a sample of early-type galaxies. Unfortunately, one cannot assume that all GALEX non-detections are smooth galaxies; of the non-detections in the gz2sample that are in the GALEX footprint (using the GALEX–SDSS–WISE Legacy Catalog of Salim et al. 2016), |$35{{\ \rm per\ cent}}$| are discs and |$29{{\ \rm per\ cent}}$| are early-type galaxies. Therefore, GALEX non-detections do not improve the morphological selection of smooth galaxies. In addition, as the bottom panels of Fig. 2 show, optical magnitudes alone do not allow for an accurate morphological classification of a sample of smooth galaxies by colour. This is particularly apparent for u − r and will affect all such works that use u − r colours to split the galaxy population morphologically. For example, Strateva et al. (2001) use a colour threshold of u − r = 2.22, which is similar to the threshold found in this study of u − r = 2.340 (see Table 1) that results in |$\sim 44{{\ \rm per\ cent}}$| of galaxies classified as early-type based on a red colour actually having featured disc morphologies.

In this work, we only assess the purity and completeness of single colour cuts. However, it is common to use a magnitude-dependent cut to divide the galaxy population. Baldry et al. (2004) fit an optimal division of u − r = 2.06 − tanh (M_r + 20.07)/1.09 that varies from u − r = 1.8, at the faint end, to 2.3, at the bright end. They caution that while this is an optimal divider, significant overlap exists in the two populations they model as Gaussian in colour. Using this division with the gz2sample results in a sample of early-type galaxies with a purity of |$56.8{{\ \rm per\ cent}}$| and a completeness of |$70.5{{\ \rm per\ cent}}$|⁠, and a late-type sample with a purity of |$82.6{{\ \rm per\ cent}}$| and a completeness of |$72.3{{\ \rm per\ cent}}$|⁠. Comparing these numbers found using the Baldry et al. division to those for a single u − r colour selection stated in Table 1 reveals that the only significant improvement is to the completeness of the sample of early-type galaxies selected, since the two-dimensional Baldry et al. threshold moves bluer than our selection for fainter galaxies. Similarly, Masters et al. (2010b), in identifying optically red spirals, use a magnitude-dependent cut of (g − r) = 0.63 − 0.02(M_r + 20), which was 1σ bluer than the main ridge of the red sequence, which revealed up to 30 per cent (at the most massive end) of even the most face-on spirals are clearly in the red sequence.

Along with colour–magnitude, the use of two colours to divide the galaxy population is also common. Examples include UV–optical combinations (e.g. NUV − r against g − r; Chilingarian & Zolotukhin 2012) and optical–NIR combinations (e.g. the UVJ diagram of V − J against U − V; Patel et al. 2012; Muzzin et al. 2013; Fang et al. 2018). Typically, the main purpose of these two-colour diagrams is to separate passively evolving galaxies from star-forming galaxies with dust-reddened optical colours. Given that subpopulations of interest such as red spirals are intrinsically red/passive rather than simply dust reddened (Masters et al. 2010b), these distinctions have limited effect on improving the use of colour as a proxy for morphological selection. For example, using a two-dimensional colour cut in NUV − u against u − r roughly reduces to a single colour cut in NUV − r, the colour we have shown is the best-performing single colour cut in this study (see Table 1). Similarly, a two-dimensional colour cut on the UVJ diagram is still highly incomplete/impure if the cut between ‘active’ and ‘passive’ from that diagram is assumed to map to late-type and early-type morphologies, respectively.

In fact, given that UVJ selection is common in higher redshift studies, the use of this two-colour selection demonstrates how issues with conflating star formation status and morphology can be exacerbated at higher redshift. If we combine Galaxy Zoo: Hubble classifications (Willett et al. 2017) with rest-frame UVJ colours and stellar masses determined by the Cosmological Evolution Survey (COSMOS)-UltraVISTA (Muzzin et al. 2013), we may examine purity and completeness using ‘clean’, debiased samples of smooth and featured galaxies analogous to the selections described in Section 2 and within a volume limit of z ≤ 1 (chosen to ensure morphologies are determined on the basis of rest-frame optical imaging) and stellar mass |$M_\ast \ge 10^9$| M_⊙. We find that assuming ‘passive’ equates to early-type results in an early-type purity of 55 per cent and completeness of 48 per cent. The late-type assumption results in considerably higher purity (88 per cent) and completeness (91 per cent), but this is dominated by the fact that at higher redshifts featured galaxies are common: if we were to assume that all galaxies were late-type regardless of colour in this ‘clean’ subsample, the selection would still be 81 per cent pure. The exact numbers depend somewhat on the lower mass limit, but the qualitative result does not change for any reasonable choice of mass cut above the flux limit. Using rest-frame optical morphologies out to z ∼ 2, an examination of UVJ versus morphology by Simmons et al. (2017) reveals a similar mixing of morphologies across the passive/active UVJ boundary, with an even larger fraction of smooth galaxies showing active star formation. We note that the practice of equating colour with morphology is much less common in high-redshift studies (e.g. see the Introduction of Schreiber et al. 2018), in part because the disconnect between these properties is more obvious at earlier epochs. The evolution of galaxy structures combined with the relatively poor mapping of colour to morphology strongly suggests there is little to be gained in the purity or completeness of a morphological sample by using a two-dimensional colour–colour or colour–magnitude selection, at any redshift.

Similarly, other morphological proxies such as FracDev, f_Dev, and Sérsic index, n, also result in impure and/or incomplete morphological samples. For example Masters et al. (2010a) demonstrate that |$45{{\ \rm per\ cent}}$| of ‘early-types’ found by f_DeV > 0.5 (the FracDev cut used by Strateva et al. 2001) are identified by Galaxy Zoo as featured discs, while |$5{{\ \rm per\ cent}}$| of the ‘spirals’ found by f_DeV < 0.5 are identified by Galaxy Zoo as smooth galaxies. Use of a single-Sérsic parameter as a proxy for bulge strength can also be challenging due to the fact that galaxies with ‘intermediate’ Sérsic values (e.g. 1.5 < n < 3) can be either bulge dominated or disc dominated (Simmons & Urry 2008; Häußler et al., in preparation). Additionally, Lange et al. (2015) find that a Sérsic index selection is the least reliable parameter for discriminating between morphological early- and late-type galaxies, compared to u − r and g − i colour cuts. Some mitigations are possible: Vika et al. (2015) found using the ratio of Sérsic indices measured in two different filters could recover half of the disc galaxies erroneously classified as early-type galaxies by a joint u − r and single-band Sérsic index selection. Morphological studies using two Sérsic parameters to simultaneously characterize bulge and disc can be more reliable than single-Sérsic fits provided there is adequate signal-to-noise ratio in the images (Simard et al. 2011), and in some cases a joint selection using both Galaxy Zoo and Sérsic-based bulge-to-total morphologies allow for selection of more pure and complete samples (Simmons et al. 2017). A joint selection capitalizes on the fact that Galaxy Zoo’s top-level ‘smooth or featured’ question does not fundamentally capture a ‘Sérsic by eye’. One additional complication is that in strongly barred disc galaxies, the presence of the bar can bias the fit making the bulge component appears larger and more concentrated (higher Sérsic index) than it is (Kruk et al. 2018).

As an alternative to the colour selection, an increasing body of work relies on machine learning to provide classifications of galaxies (e.g. Huertas-Company et al. 2015; Beck et al. 2018; Domínguez Sánchez et al. 2018; Walmsley et al. 2020; Vavilova et al. 2021). Though early examples date from nearly 30 yr ago (Storrie-Lombardi et al. 1992), the development of neural networks was a significant breakthrough. The first application to galaxy classification by Ball et al. (2004) found that the highest values of correlation between T-type and input parameters, including properties such as radius, surface brightness, and concentration, were with colour, an early indication of the propensity of the correlation between colour and morphology to influence machine learning classifications. This property is particularly seen in more recent deep learning implementation by, amongst others, Dieleman, Willett & Dambre (2015), Domínguez Sánchez et al. (2018, 2019), and Vavilova et al. (2021). Vavilova et al. (2021) claim that their supervised machine learning algorithm trained over SDSS photometric parameters is less biased than when trained using Galaxy Zoo visual morphologies. However, their measurement of bias is based on the correlation of the morphologies with colour and concentration, exactly the assumption we are concerned to avoid making here.

The correlation between colour and morphology makes it a confounding variable in machine learning solutions; without training on monochrome images or the development of a specialized figure of merit, any supervised network is likely to quickly learn the apparent rule that colour implies morphology. For example, Hocking et al. (2015) used an unsupervised learning technique to split late- and early-types in cluster survey images; again with colour being the dominant property that the machine used to classify. Hocking et al. (2015) discuss how galaxies identified as early-types by their algorithm include those spirals with bulges with redder colours, and those galaxies identified as late-types included lensed features with bluer colours. Such careful reflection on results demonstrates the issues that arise when an algorithm uses colour as a proxy for morphology.

On the other hand, when morphology and colour are used independently as (imperfect) measures of dynamics and star formation, new results often emerge. For example, Nair, van den Bergh & Abraham (2010) find that colour and morphology have different effects on both the slope and dispersion of local luminosity–size relations for galaxies. Investigating quenching, Schawinski et al. (2014) separate the local (SDSS) colour–magnitude diagram by visual morphology (using the same ‘clean’ samples that we have used here) and find that the green valley can be understood as the overlap of the tails of the two morphological populations. Incorporating a simple model of star formation history using NUV–optical colours, Schawinski et al. also find that discs and spheroids evolve very differently across the green valley. With Bayesian modelling of star formation histories from galaxy colours and incorporating the full galaxy population (including intermediate morphologies) using Galaxy Zoo morphologies to provide probabilistic weighting, Smethurst et al. (2015) uncover further nuance in the quenching histories of smooth and featured galaxies (e.g. revealing an intermediate quenching mode that can occur both with and without morphological transformation), which would have remained hidden had colour been used as a proxy for morphology. In an examination of galactic conformity that (for the first time in this field; cf. Weinmann et al. 2006; Prescott et al. 2011) considers morphology and star formation fully independently, Otter et al. (2020) find that star formation and morphological conformity are different. Specifically, they find that morphological conformity is weaker than star formation conformity, which is consistent with a physical model wherein star formation properties change more rapidly (or more readily) than galaxy dynamics in the group environment. Another example is the discovery that red discs host significantly more bars, which Masters et al. (2011) argue had been previously missed in part due to pre-selection of ‘disc’ samples to include only blue discs. Results such as these offer a glimpse into the potential of independently examining morphology and star formation rate, in addition to the results on passive red spirals and blue ellipticals already discussed above.

The wide availability of Galaxy Zoo morphologies for a variety of imaging surveys² means that any selection a researcher decides must be made using colour can be checked for purity and completeness with quantitative visual morphologies. For most investigations into galaxy evolution where both colour and morphology are involved, we would strongly suggest using morphology as an independent quantity wherever possible. If quantitative visual morphologies are not available for a particular sample, a combination of parametric and/or non-parametric morphologies may be used (potentially in combination with colour) to increase a sample’s purity and completeness.

5 CONCLUSIONS

We have investigated the purity and completeness of galaxy samples constructed using a single colour cut as a proxy for morphology. We determined the values of purity and completeness that can be achieved using a given colour threshold for colours across optical (SDSS; ugriz), ultraviolet (GALEX; NUV), and infrared (2MASS; JHK) surveys. We focus only on single colour cuts in this study (however see Section 4 for a discussion on the addition of magnitude, a second colour, or other morphological proxies) and determine the colour threshold at which a reasonable compromise between purity and completeness can be achieved. We choose to examine the value where purity and completeness are equal, as this single value being higher typically indicates a higher fidelity in the assumption that colour and morphology are good proxies of one another.

We find that NUV − r achieves the best compromise between morphological purity and completeness within a sample. Using a colour threshold of NUV − r = 4.961 results in a sample of early-type galaxies with a purity and completeness of |$65.8{{\ \rm per\ cent}}$|⁠, and for late-type galaxies of 92.8 per cent.

Without the addition of NUV magnitudes, optical colours used as a proxy for morphology result in less pure and less complete samples. Using a threshold of g − r = 0.742 results in an early-type galaxy sample with a purity/completeness of only |$56.6{{\ \rm per\ cent}}$|⁠, and a late-type galaxy sample with purity/completeness of |$76.3{{\ \rm per\ cent}}$|⁠. We also find that no improvement is found by adding NIR magnitudes to the optical bands. We note that with any two magnitude bands, including NUV, a sample of early-types with greater than two-thirds purity cannot be constructed.

We therefore conclude that when colour is used as a proxy for morphology impure and incomplete samples are the result. If no other option beyond a colour cut is available, either (1) samples should not be interpreted as morphologically homogeneous, or (2) the morphological make-up of colour-selected samples should be measured, e.g. using publicly available Galaxy Zoo morphologies (see Footnote 2).

The relative simplicity of quantifying colour in large surveys, versus the complexity of morphology, presumably contributed to the large-scale uptake of conflating colour with morphology. While this has allowed for many significant advances in our understanding of the general galaxy population, further progress requires that we more explicitly separate stellar dynamics from star formation by incorporating the visual morphology of galaxies into our analyses. The problem of generating high-quality, quantitative (i.e. having an estimate of error) visual morphologies for large samples of galaxies was solved over a decade ago with the Galaxy Zoo methodology (Lintott et al. 2008), which is now being extended to work for larger and larger samples by an optimal partnership between the crowd and machines using adaptive learning (Walmsley et al. 2022). Similarly, supervised and unsupervised machine learning have advanced in recent decades to produce purer and more complete morphological samples than using colour alone. In addition, non-parametric morphological classifications, such as concentration and asymmetry (e.g. Abraham et al. 1994, 1996; Tohill et al. 2021) and the Gini coefficient and M₂₀ (Lotz, Primack & Madau 2004), have provided an automated way of morphologically constraining large samples of galaxies. Therefore, the main reasons that the community moved to widespread use of colour as a proxy for morphology within the galaxy population are no longer valid. With upcoming large-scale extragalactic surveys poised to deliver a variety of robust morphological measures alongside precise multiband photometry, we anticipate new discoveries about galaxy evolution from the careful consideration of these independent quantities.

ACKNOWLEDGEMENTS

ILG and DO’R acknowledge support from STFC studentships at Lancaster University (grant number ST/T506205/1). BDS acknowledges support from a UKRI Future Leaders Fellowship, administered by the Medical Research Council (grant number MR/T044136/1).

This publication uses data generated via the Zooniverse.org platform, development of which is funded by generous support, including a Global Impact Award from Google, and by a grant from the Alfred P. Sloan Foundation. This publication has been made possible by the participation of hundreds of thousands of volunteers in the Galaxy Zoo project on Zooniverse.org.

This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This publication makes of use data from GALEX. GALEX is a NASA mission managed by the Jet Propulsion Laboratory. This publication uses data from the Sloan Digital Sky Survey (SDSS-I/II). Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS website is http://www.sdss.org/.

DATA AVAILABILITY

All data used in this paper are publicly available at the locations we cite.

Footnotes

REFERENCES

Author notes