Identifying AGNs in Low-mass Galaxies via Long-term Optical Variability

Straightforward aperture photometry is insufficient for detecting low-level variations in the light output of a galaxy nucleus. Given that each night of observation has different seeing, simply measuring the flux within a constant aperture means that each observation contains a different fraction of the galaxy starlight in that aperture. The counts measured within a constant aperture depend strongly on the seeing.

Thus, we use difference imaging to construct light curves for each galaxy. Difference imaging, or image subtraction, involves convolving a template image with a kernel to match the seeing and background of an individual observation, and then subtracting one from the other to create a diff.pdference image. Specifically, we use the difference imaging software Difference Imaging Analysis Pipeline 2 (DIAPL2),⁵ which is a modified version of the Difference Imaging Analysis software introduced by Wozniak (2000). Both are implementations of the basic algorithm introduced by Alard & Lupton (1998) and Alard (2000). The basic steps of our difference imaging procedure are listed below; steps 2 through 4 are carried out within DIAPL2.

• 1.  
  Crop the SDSS field images to cutouts of 800 × 800 pixels (53 × 53) centered around the NSA galaxy. Since fields in different epochs are centered differently, adjacent fields sometimes must be stitched together and then cropped.
• 2.  
  Align the images, correcting for small pixel shifts between individual frames.
• 3.  
  Construct a template image consisting of the frames with the best seeing and lowest background. We chose 30% of the frames to be used in the template.
• 4.  
  For each individual exposure, convolve the template image with a best-fit kernel to match the seeing of the exposure. The kernel is a sum of 2D Gaussians of different widths, and the best-fit parameters are found through chi-squared minimization. The convolved template is then subtracted from the exposure to create the difference image.
• 5.  
  Construct a light curve using forced photometry of template and difference images. Since we are searching for variability from a point source, photometry is done on a 25 circle at the position of the galaxy nucleus as defined in the NSA. The 25 aperture is chosen to be slightly larger than the worst-case scenario seeing, so as not to miss any light from the galaxy nucleus. The flux value for each epoch is the value measured in the template plus that measured in the difference image.

AGN light curves are well-modeled by a damped random walk (Kelly et al. 2009; MacLeod et al. 2010, 2011; Butler & Bloom 2011). The damping functions to push deviations back toward a mean value, as opposed to the variance simply continuing to increase over time.

After constructing each light curve, we use the Butler & Bloom (2011) quasar fitting software qso_fit⁶ to determine whether the light curves are variable, and whether the observed variability is characteristic of an AGN. Butler & Bloom (2011) define a covariance matrix C which well-describes AGN variability as a function of time. It is then possible to write down the probability of observing some data x given the AGN variability model C. Specifically, the qso_fit code creates a model light curve by modeling each point given the other points and the covariance matrix describing the variability. It then assesses how well the best-fit damped random walk model describes the data.

We compute several fit statistics, including χ²/ν (standard measure of variability), [χ²/ν]_QSO (the fit statistic for the fit of the data to a damped random walk model), and [χ²/ν]_null (the expected fit statistic for a non-AGN variable source). We also compute σ_var (the significance that the source is variable), σ_QSO (the significance that [χ²/ν]_QSO < [χ²/ν]_null), and σ_notQSO (the significance the source variability is not AGN-like).

First, we select objects with a variability significance σ_var > 2 and a QSO significance σ_qso > 2 (i.e., the significance that the source is variable and that the fit to the damped random walk model is better than the fit to a randomly variable model are >2σ). Of the 28,062 total galaxies with light curves, 201 meet these AGNs variability selection criteria.

We then inspect light curves by eye to remove objects that are identified as variable due to poor image subtractions or likely supernovae (SNe) missed by the variance and QSO light curve cuts. Of the 201 galaxies that initially meet our selection criteria, we find that 29 of them are SN-like (i.e., show one frame with a bright nucleus, or an obvious rise and fall on a SN-like timescale), 15 are mischaracterized in some way in the NSA (i.e., are either stars or higher-redshift AGNs), and 21 have problematic image subtractions, such as interference from a nearby saturated star. One system—NSA 29189—has AGN-like variability but is classified in the literature to contain a luminous blue variable star (Izotov & Thuan 2009). This leaves 135 variability-selected AGNs. In Figure 2 we show examples of galaxies with AGN-like variability. Figure 3 shows examples of objects with variable light curves uncharacteristic of an AGN, and Figure 4 shows galaxies initially classified as AGNs that have SN-like light curves.

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Figure 5 shows a two-dimensional histogram of light curve standard deviation (σ_LC) versus median nucleus magnitude (with the nucleus defined as the central 25). The light curve standard deviation corresponds to the 1σ scatter about a light curve median value. All of the objects identified as variable AGNs by our criteria also happen to have σ_LC more than one standard deviation above the typical σ_LC for nuclei of the same magnitude.

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3.2.1. Other Variable Objects

We analyze SDSS spectroscopy for our variability-selected AGN. If a galaxy has more than one spectrum, we use the primary spectrum designated by the SDSS. In particular we measure emission-line fluxes and search for broad Hα emission potentially indicative of dense gas orbiting around a central BH. Here, we describe the emission-line modeling procedure (see also similar fitting procedures described in Ho et al. 1997; Greene & Ho 2004; Reines et al. 2013; Baldassare et al. 2015, 2016).

We first create a model for the narrow-line emission using the intrinsically narrow [S ii] λλ6713 and 6731 lines. As these are forbidden transitions, they are guaranteed not to be produced in the denser broad-line region gas. This narrow-line model is then used to fit the narrow Hα emission and the [N ii] λλ6548 and 6684 lines simultaneously. We allow the width of narrow Hα to increase by up to 25% and fix the relative amplitudes of the [N ii] lines to laboratory values. Next, an additional Gaussian component representing the broad Hα emission is added to the model. If the χ² value of the fit improves by 20%, the broad component is kept in the model. We allow up to two Gaussian components to be used to model the broad emission.

We also fit Hβ, [O iii] λ5007, [O iii] λ4959, and the [O ii]λλ3726,3729 doublet. We also allow Hβ to be fit with an additional (broad) Gaussian component. In all of our emission-line fitting, the continuum is modeled simply as a line across the relevant spectral region.

The host galaxies of the variability-selected AGNs range from ∼2 × 10⁸ to 5 × 10¹¹ M_⊙ in stellar mass. Figure 6 shows the stellar mass distribution of the 135 variability-selected AGN hosts as compared to the parent sample of ∼28,000 galaxies in the NSA for which we construct light curves. The variability-selected AGNs tend toward higher stellar mass; the median stellar mass of the variability selected AGNs is 1.8 × 10¹⁰ M_⊙, while the parent sample has a median stellar mass of 6.8 × 10⁹ M_⊙. We show the host galaxy g − r colors in Figure 7. The g − r colors of the variability-selected AGNs range from 0.01 to 1.1, and as a sample tend to be bluer than the parent population (see also Matsuoka et al. 2014).

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The properties of the NSA/Stripe 82 AGNs identified in this work are consistent with those found for a sample of 975 variability-selected AGNs from the Pan-STARRS1 Medium Deep Survey, which consists of 10 7-deg² fields imaged in the same filter every three nights (Heinis et al. 2016) down to a limiting magnitude of ∼23.5. To compile their sample of AGNs, they began with a sample of 4361 extragalactic variable sources, which were then further classified as AGNs or SNe (Kumar et al. 2015). While not all objects in their sample have spectroscopic information, they find that the masses of the variability-selected AGN skew high as compared to the general population of galaxies. Their distribution of host galaxy masses peaks near ${\mathrm{log}}_{10}({M}_{* }/{M}_{\odot })=10.6$, similar to our results (Figure 6). They also find that their AGN hosts tend to be bluer than the general population.

We show where the variability-selected AGNs sit on the Baldwin–Phillips–Terlevich (BPT) diagram (Baldwin et al. 1981) in Figure 8. We plot only galaxies which have signal-to-noise ratio ≳ 2 for all of Hβ, [O iii] λ5007, Hα, and [N ii] λ6584 (104 galaxies). Of the 104 galaxies, 86 of them (83%) have narrow emission-line ratios placing them in the AGN or composite regions of the BPT diagram (21 BPT composites and 65 BPT AGNs). Interestingly, 18 galaxies (or 17% of the spectroscopic sample) have narrow emission-line ratios dominated by star formation. These galaxies tend to be the lowest-mass systems in our sample. Only two of the 18 in the star-forming region have stellar masses greater than 10¹⁰ M_⊙; the median stellar mass for these 18 objects is 1.7 ×10⁹ M_⊙.

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We also search for broad Hα emission indicative of dense gas orbiting around the central BH. We find that 82/135 of the galaxies with AGN-like variability (61%) have broad Hα emission lines. Of the objects with narrow lines in the composite/AGN regions, ∼80% also show broad Hα. We estimate single-epoch virial BH masses using the broad Hα FWHM and luminosity (Greene & Ho 2005). The FWHM of the broad component gives a characteristic velocity of gas in the broad-line region, and the distance to this region is correlated with the continuum luminosity at 5100 Å (Bentz et al. 2009, 2010, 2013), which in turn is correlated with the luminosity of broad Hα. BH masses estimated in this way have systematic uncertainties of roughly 0.3 dex (or a factor of ∼2). Specifically, we use the BH mass formula given in Reines et al. (2013). The broad Hα luminosities range from ∼1 ×10³⁹ to 3 × 10⁴² erg s⁻¹ and the FWHMs range from ∼900 to 6500 km s¹. We calculate BH masses ranging from from 1 × 10⁶ to 1 × 10⁸ M_⊙, and the median M_BH-to-M_* ratio is 8 × 10⁻⁴, close to the canonical value of 0.001 (Kormendy & Ho 2013). However, there is considerable scatter about this value, as shown Figure 9. Fitting a linear regression to the M_BH-to-M_* relation for these objects gives a slope that is consistent with zero.

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We present the measured active fraction (i.e., the fraction of galaxies with AGN-like variability) as a function of stellar mass in the left panel of Figure 10. At face value, Figure 10 suggests that there is a steep increase in the fraction of variable AGNs as a function of stellar mass. However, there are a number of observational biases which must be taken into account. As shown in Figure 5, lower levels of variability are detectable in brighter nuclei. The median nucleus g-band magnitude for the M_* >10¹⁰ M_⊙ sample is ∼18.5, while for galaxies with M_* < 10¹⁰ M_⊙ the median magnitude is ∼19.5. The right side of Figure 10 shows the active fraction as a function of nucleus g-band magnitude for two different mass bins. At a given nucleus magnitude, the active fraction tends to be lower for low-mass galaxies than for higher-mass galaxies (see Section 6 for a discussion of potential explanations). At m_g ≈ 18, the variable AGN fraction is roughly twice as high in the sample with M_* > 10¹⁰ M_⊙ than for the low-mass sample (Table 2).

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In order to determine what population of BHs we are sensitive to, in this section we explore the AGN detection limit for the low-mass sample, given the depth of the SDSS observations and the difference imaging technique. For each light curve, we compute the median nuclear g-band magnitude and the standard deviation of the individual measurements about the median magnitude (σ_LC). Thus for a given magnitude bin, we can compute the median light curve standard deviation of objects in that bin. For example, the median σ_LC for nuclei with an apparent g-band magnitude of 18 is 0.01 mag. For nuclei with apparent g-band magnitude of 20, the median σ_LC is 0.035 mag. The nuclei selected as having AGN-like variability all have light curve standard deviations ≳1σ above the median σ_LC for their magnitude bin (see Figure 5).

We next compute the typical galaxy magnitude within the 25 nuclear aperture as a function of redshift. For a given redshift bin, we use the median Sérsic profile index (as given by the NSA) to determine the typical fraction of galaxy light contained within 25. We then use this value to compute the typical g-band magnitude within 25. As mentioned above, each magnitude has a light curve standard deviation value above which the objects classified as AGNs are found. For each redshift, we convert the variations in the apparent magnitude to variations in the luminosity. Then, assuming that the observed variations are on order 10% or 50% of the total AGN luminosity, we compute the total g-band luminosity an AGN would need to have to be detectable in a typical galaxy of a given stellar mass as a function of redshift (top panels of Figure 11).

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We stress that this analysis comprises a rough estimate of our detection limits—at any stellar mass, there exist galaxies with a wide range of Sérsic indices and luminosities and thus a range of AGN luminosities/BH masses that could be detected. Nevertheless, based on this calculation, we can roughly expect to detect a ∼10⁵ M_⊙ BH in a low-mass galaxy accreting at its Eddington luminosity and varying at the 10% level out to z ≈ 0.05. For luminosity variations on the 50% level, the same should be detectable to z ≈ 0.1.

We next explore how many variable AGNs we could expect to detect in our M_* < 10¹⁰ M_⊙ sample, given local scaling relations between BH mass and the host galaxy. Using the relations between BH mass and stellar mass from Reines & Volonteri (2015), we assign each galaxy a BH mass given its stellar mass in the NSA (and given the intrinsic scatter in the M_BH–M_* relation). Reines & Volonteri (2015) find different M_BH–M_* relations for inactive elliptical/S0 galaxies and local active broad-line AGNs; we test both relations. For each of the M_BH–M_* relations, we then compute bolometric luminosities by applying the Eddington ratio distribution given by Bernhard et al. (2018) for low-mass galaxies (10⁸–10¹⁰ M_⊙). We can then determine how many galaxies would be detected, assuming the g-band luminosity is 5% of the total bolometric luminosity, and luminosity variations at the 10% or 50% level.

In Figure 11, we show the minimum detectable AGN luminosity (as discussed in the previous section), along with examples of simulated BH samples given both M_BH–M_* relations and luminosity variation level. We also show the histograms of the number of detected AGNs for 100 simulated samples using each combination of M_BH–M_* relation and luminosity variation level. For BH masses populated according to the M_BH–M_* relation for elliptical/S0 galaxies, we expect to detect 92 ± 10.4 variable AGNs for variations at the 10% level, and 264 ± 15.6 for 50% variations. For BH masses populated according to the M_BH–M_* relation for local active galaxies, we expect to detect 13.5 ± 3.6 for 10% variations, and 58 ± 7.6 for 50% variations. Our detected number of low-mass galaxies with AGN-like variability—35—is more closely in line with the number expected based on the M_BH–M_* relation for active galaxies.

One of the most effective techniques for identifying AGNs in low-mass galaxies is optical spectroscopy. Reines et al. (2013) searched for AGNs in dwarf galaxies (defined as galaxies with M_* < 3 × 10⁹ M_⊙) in the NSA using optical narrow emission-line ratio selection criteria. Of ∼25,000 dwarf galaxies, 136 had narrow emission-line signatures indicative of AGN activity, for a detection fraction of 0.5%. Ten of them also had broad Hα emission, with BH masses ranging from 8 × 10⁴ to 1 × 10⁶ M_⊙. Our sample contains 8941 galaxies with M_* < 3 × 10⁹ M_⊙, 12 of which have AGN-like variability. This gives a variability detection fraction of 0.1%. Of the 12 dwarf galaxies with AGN-like variability, one (NSA 32653) has narrow emission-line ratios in the AGN region of the BPT diagram and shows broad Hα emission (M_BH = 6 × 10⁶ M_⊙). It was not selected in Reines et al. (2013), as that work used the NSA v0, which only extends out to z = 0.055.

Moran et al. (2014) also used optical spectroscopy to search for AGNs in low-mass galaxies. Specifically, they searched for AGN signatures in galaxies with M_* < 10¹⁰ M_⊙ within 80 Mpc. Overall, they detected AGNs in 28/9526 galaxies, for a detection fraction of 0.29% (similar to our detection fraction of 0.22%). Of their 28 galaxies, seven have stellar masses in the regime considered by Reines et al. (2013), five of which are also classified as AGNs in that work. When considering just galaxies with stellar masses between 4 × 10⁹ and 10¹⁰ M_⊙, their detection fraction is 2.7%. The Moran et al. (2014) AGN host galaxies have a median g − r color of 0.62, slightly redder than our sample.

There are six dwarf galaxies with narrow emission-line evidence for AGN activity from Reines et al. (2013) which fall inside the area covered by the Stripe 82 survey (none of the Moran et al. 2014 objects fall within Stripe 82). None is classified as having nuclear variability according to our selection criteria. One of the six galaxies (RGG 1 in Reines et al. 2013) has broad Hα emission, from which we can obtain a BH mass estimate. RGG 1 is at a redshift of 0.046 and has a stellar mass of 2.6 × 10⁹ M_⊙. The BH mass reported in Reines et al. (2013) is 5.0 × 10⁵ M_⊙ (note that systematic uncertainties on BH masses derived from broad Hα are on the order of ∼0.3 dex). Using Chandra X-ray observations, Baldassare et al. (2017b) find that this BH is accreting at 0.001 L_Edd. Using the same assumptions as the previous section, this BH would have a g-band luminosity of 3.0 × 10³⁹ erg s⁻¹. As shown in Figure 11, at a redshift of 0.05, we are sensitive to AGNs with g-band luminosities greater than ∼10⁴¹ erg s⁻¹. Therefore, we would not expect to detect any variability from this AGN (see Figure 11).