TOWARD PRECISION SUPERMASSIVE BLACK HOLE MASSES USING MEGAMASER DISKS

We apply two selection criteria. First, we use the stellar velocity dispersion measurement from HETMGS to roughly estimate whether or not a dynamical BH measurement will be possible. Specifically, the gravitational sphere of influence of the BH (${\theta }_{{\rm{I}}}\propto \frac{{{GM}}_{{\rm{BH}}}}{D{\sigma }_{*}^{2}};$ where D is the distance) needs to be spatially resolved (${\theta }_{{\rm{I}}}\gt 0\buildrel{\prime\prime}\over{.} 06$) in order to probe regions near the BH. Since we have no measurement of the BH mass, we use ${M}_{\mathrm{BH}}$ $\propto \quad {\sigma }_{*}^{4}$ from Gültekin et al. (2009) as a proxy.⁶ There are 369 such galaxies in the HETMGS.

Second, we only select galaxies with optical signs of nuclear activity. Ideally, we would search all 369 galaxies with ${\theta }_{{\rm{I}}}\gt 0\buildrel{\prime\prime}\over{.} 06$, but in order to boost the probability of finding a maser disk, we restricted our attention to galaxies with optical signatures of accretion. We use the HETMGS spectra⁷ to measure strong emission lines ratios [N ii]$\quad \lambda 6583$/H_α and [O iii]$\quad \lambda 5007$/H_β. Standard Baldwin, Phillips, & Terlevich (BPT: Baldwin et al. 1981) diagnostic diagrams are used to isolate the active galactic nuclei (AGNs; Figure 1) from the galaxies with (nuclear) star formation. Selecting only the AGNs further reduces the target list to 121 objects. For this search, we did not distinguish between Seyferts and low-ionization nuclear emission region LINERs (Heckman et al. 1981), but see Section 3.4.

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Finally, we checked for overlap between the HETMGS and the GBT searches. After removing all galaxies previously searched for megamaser emission, 93 galaxies remained in our target list. This last cut removed almost all of the bright AGNs from our target list. See Figure 1 for the distribution in the BPT diagram of the observed galaxies.

We conducted our survey using the K-Band Focal Plane Array (KFPA) and the GBT Spectrometer. We used two beams of the KFPA in the same mode used by the MCP. We used two IF's of 200 MHz bandwidth offset by 180 MHz, for a total coverage of 380 MHz. Each window covers 2800 km s⁻¹ and with overlap the total coverage is 5100 km s⁻¹. We do not know a priori the velocity extent of the putative megamaser disks in these more massive galaxies. However, if we had detected only systemic masers in any system, we would have expanded the search to higher velocities. We used a total-power observing mode, nodding the telescope to alternate the target galaxy between the two beams on a 2.5-minute interval. The receiver pointed off source is used as the reference beam to measure the background. The reference beam spectrum is smoothed with a kernel of 16 channels, to increase its signal-to-noise. In good weather (${T}_{\mathrm{sys}}\sim 40$ K) and integrating 10 minutes per galaxy, we achieved ∼4 mJy rms per channel after Hanning smoothing. The pointing corrections, done roughly each hour, were typically 5'' or better, and the flux calibration is accurate to about 20%. The final velocity resolution and channel spacing is 0.4 and 0.3 km s⁻¹. This observing setup is sufficient to identify any megamasers that can be imaged in follow-up observations with a single VLBI track.

We observed 87 galaxies using 21.5 hr during a visit to the NRAO's GBT⁸ from 6 through 2012 November 15 as program GBT/12B-052. See Table 1 with observations of this HETGBT sample. Apart from galaxies from our target list, the 87 galaxies include five filler objects and the control maser NGC 6240. The filler objects have properties close to our selection criteria and are included in our HETGBT sample. At our maximum distance of 130 Mpc, the 3σ luminosity limit is ∼0.7 ${L}_{\odot }$, while the least luminous known H₂O masing disk is in NGC 2273, which has an isotropic luminosity of 23 ${L}_{\odot }$, so we are not limited by sensitivity.

The sample has a median distance of 74 Mpc and a median stellar velocity dispersion of 250 km s⁻¹. The majority of the sample galaxies are elliptical galaxies (see the next paragraph), with likely BH masses in excess of 10⁸ ${M}_{\odot }$. Since the sphere of influence depends steeply on ${\sigma }_{*}$, our sample is heavily skewed toward high-dispersion galaxies. As shown in Figure 2, our program more than doubles the number of galaxies with $\sigma \gt 250$ km s⁻¹ that have been surveyed for maser emission with the GBT. The observed galaxies have larger inferred spheres-of-influence than the galaxies previously searched as well. As shown in Figure 2, this survey doubles the number of galaxies searched with ${\theta }_{{\rm{I}}}\gt 0\buildrel{\prime\prime}\over{.} 06$.

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Only 44 objects have a morphological type T in Hyperleda (Paturel et al. 2003). Almost all of these are ellipticals: $T=-3.2\pm 1.9$. The only known spiral in our sample is IC 0356. In general, we do not have deep and reliable imaging with which to determine Hubble types. Thus, to put the morphological distribution of our sample into context, we plot the mass–size relation of all galaxies searched for masers by the GBT. Ellipticals obey a tight scaling between size and mass and are the smallest (densest) galaxies at a given stellar mass. As Figure 3 shows, the HETMGS galaxies that we searched preferentially probe dense elliptical galaxies, while previous searches were overwhelmingly dominated by spiral galaxies. Our search probes the locus of early-type galaxies and adds to a part of parameter space that has not yet been exhaustively searched.

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There was a large survey of elliptical galaxies carried out by Henkel et al. (1998), but it was focused on luminous radio galaxies, so it selected galaxies in a different way from this search. Indeed, there are only a few known megamasers in elliptical galaxies: NGC 1052 (Braatz et al. 1994; Tarchi et al. 2003), 3C403 (Tarchi et al. 2007), Centaurus A (Ott et al. 2013), possibly NGC 2960 (Kormendy & Ho 2013). Object TXS2226-184 is most likely not an early-type galaxy (Falcke et al. 2000). About half of our sample is detected in NVSS (NRAO VLA Sky Survey), with a median luminosity of 10 mJy (Condon et al. 1998).

As described above, the largest current megamaser disk search with uniform sensitivity has been carried out by the GBT. We combine the full list of galaxies searched by the GBT with our smaller list to search for trends between detections and optical properties of the galaxies. To maximize the number of searched galaxies with literature optical spectroscopy, we rely on the Sloan Digital Sky Survey (SDSS). A. Constantin et al. (2015, in preparation) started with the 3339 maser non-detections as of 2013 June, along with 151 galaxies with maser detections. They cross-matched these galaxies with the SDSS (York et al. 2000) and the Palomar Survey of nearby galaxies (Ho et al. 1997a). There are spectroscopic matches for 1330 of the non-detections, and 92 of the maser galaxies, which include 15 maser disks. From these matches, we have measurements of stellar velocity dispersion (${\sigma }_{*}$), and emission-line properties, including the Balmer decrement and the [O iii] luminosity corrected for extinction. We will also discuss measurements of the maser luminosities, which typically fall in the range of tens to thousands of solar luminosities for megamasers. These represent the luminosity that the maser system would have if it were isotropic. The true luminosities are very uncertain, as they are highly dependent on the (generally unknown) beaming distribution (Kuo et al. 2011).

We should also note that there may well be subtle biases in the galaxies that have been targeted spectroscopically by the SDSS. These biases are then imprinted on the subset of targeted galaxies presented here. For instance, heavily reddened galaxies may be less likely to fall into the SDSS main galaxy sample (Strauss et al. 2002). More massive galaxies are also less likely to be targeted spectroscopically at very low redshift (e.g., Fukugita et al. 2007). Therefore, we should be wary of jumping to very strong conclusions until these biases are also studied and accounted for (A. Constantin et al. 2015, in preparation).

Both Zhu et al. (2011) and Constantin (2012) pointed out a rising fraction of megamaser galaxies as the galaxy stellar velocity dispersion rises. However, there are very few galaxies in their samples with ${\sigma }_{*}$ $\gt \quad 160$ km s⁻¹. Nearly all of our galaxies fall in this high-dispersion regime. In Figure 4 (left), we show the maser fraction as a function of ${\sigma }_{*}$ prior to our survey (long-dashed lines) as well as the detection fraction after adding all of our non-detections (solid). Unfortunately, just based on Poisson errors alone, we still do not have enough data in the high-dispersion bins to make a significant measurement of the maser fraction at high dispersion. However, it is clear that the continued rise in the detection fraction above ${\sigma }_{*}$ $\approx \;150$ km s⁻¹ is not real. If we restrict our attention to the megamaser disk galaxies alone, then we still see a rise toward ${\sigma }_{*}$ $\approx \;150$ km s⁻¹, but the measurements at low dispersion are also highly uncertain due to small numbers.

Apart from the dependence on velocity dispersion, the trend seen most clearly in Zhu et al. (2011) and Constantin (2012) is an increased detection fraction at higher [O iii] luminosity. Recall that in Seyfert galaxies, the [O iii] luminosity is an indirect indicator of the bolometric luminosity of the AGN (e.g., Yee 1980), and is often used when the non-thermal continuum cannot be directly measured (e.g., Zakamska et al. 2003; Heckman et al. 2004; Liu et al. 2009).

In Figure 4 (right) we again show the maser and maser disk detection fractions for the sample of galaxies searched by the MCP. The trend toward higher detection fraction at higher [O iii] luminosity is quite clear in this case, even excluding uncertain bins. Because we do not have accurate measurements of the [O iii] luminosity for the HETMGS sample, we do not include them. The 10 HETGBT galaxies with SDSS spectra would fall at the faint end of the distribution, with ${L}_{[{\rm{O}}{\rm{III}}]}\approx 5\times {10}^{37}$ erg s⁻¹. From this figure alone, one might conclude that our non-detections are due entirely to the luminosity distribution of the sources we targeted. If megamaser disk luminosity and AGN bolometric luminosity are correlated (e.g., Henkel et al. 2005; Kondratko et al. 2006b) then perhaps we simply did not have the sensitivity to detect the possibly very faint masers around these very weak AGNs.

However, we suggest that there is more to the story. Examination of Figure 5 reveals that while there is a weak correlation between the maser luminosity and ${L}_{[{\rm{O}}{\rm{III}}]}$ when looking at all maser sources, this correlation vanishes for the maser disk sources taken alone. Instead, they span a very narrow range in isotropic maser luminosity that is virtually independent of ${L}_{[{\rm{O}}{\rm{III}}]}$. A similar trend can be seen when looking at a function of hard X-ray luminosity in Kondratko et al. (2006a); most of the correlation is driven by the non-disk masers. At the same time, our typical ${L}_{[{\rm{O}}{\rm{III}}]}$ luminosity is well below the typical luminosity for known megamaser disks (including NGC 4258). Perhaps we are detecting a true threshold in luminosity, below which the temperature condition for masing (∼400 K e.g., Neufeld et al. 1994) is not met. An ${L}_{[{\rm{O}}{\rm{III}}]}\approx {10}^{38}$ erg s⁻¹ corresponds roughly to ${L}_{{\rm{X}}}\quad \approx$ 10⁴⁰–10⁴¹ erg s⁻¹, depending on the bolometric correction and the assumed dust correction for ${L}_{[{\rm{O}}{\rm{III}}]}$ (Vasudevan & Fabian 2007; Liu et al. 2009; Shao et al. 2013). This threshold, which lies below the observed X-ray luminosity of known maser disks (Kondratko et al. 2006a), is roughly consistent with the calculations of Neufeld et al. (1994). In Section 4, we discuss in more detail the physical connection between luminosity, BH mass, and disk size that may cause the dearth of masers we observe.

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We can also ask whether the detection fraction depends on the type of nuclear activity that we observe. In particular, while line ratios associated with high-ionization Seyfert galaxies are difficult to achieve through any mechanism other than accretion onto an SMBH, LINER activity has a wide array of causes, including shocks (see a review in Ho 2008). Particularly in large-aperture data, previous studies (Sarzi et al. 2006; Singh et al. 2013) have shown that the central LINER emission often does not arise directly from an AGN. Our HETGBT sample contains equal numbers of LINERs and Seyferts and almost all are low luminosity, as indicated by the low amplitude-over-noise of the emission lines (van den Bosch et al. 2015).

The majority of the megamaser detections are found in Seyfert galaxies (see Figure 1), likely because many of the LINERs in the SDSS are not actually powered by nuclear accretion. On the other hand, NGC 4258 is a LINER, so we had some hope that a survey focused on low-luminosity systems like NGC 4258 would have a higher yield (Ho et al. 1997b). That was not the case. We conclude that it is more important to select galaxies above the possible X-ray luminosity threshold than to worry directly about the optical line ratios.

It is easy to imagine that the megamaser luminosity will correlate with the luminosity of the AGN on average (Neufeld 2000). It is the X-ray corona that most likely heats the molecular accretion disk, thus creating a metastable population of excited water molecules that are able to mase (Herrnstein et al. 2005). A weak correlation is seen between hard X-ray luminosity and megamaser luminosity when all megamaser AGNs are considered (Kondratko et al. 2005), as well as a correlation between megamaser luminosity and FIR luminosity (Henkel et al. 2005). Furthermore, it is clear from Figure 4 that the detection fraction of megamasers in general, and maser disks in specific, both rise at higher [O iii] (and therefore bolometric) luminosity. However, as argued above, given the lack of correlation between megamaser disk luminosity and AGN luminosity (Figure 5), we find it unlikely that our non-detections can be explained by the presence of very faint masers around our very low luminosity AGN. We favor the possibility that there is a threshold ${L}_{{\rm{X}}}\approx {10}^{40}$ erg s⁻¹, below which the conditions for masing are no longer met. Specifically, the size of the maser disk required at low accretion rates and high BH masses may simply grow too large to be stable.

According to Neufeld et al. (1994), masing disks are expected to have a very constant surface luminosity density. We thus expect the outer radius of the disk R_cr, set by the transition from a molecular to atomic disk, to scale with the X-ray luminosity (Kondratko et al. 2006a). Such a scaling is observed by Wardle & Yusef-Zadeh (2012). Let us now imagine that we take NGC 4258 as a model for the maser disks that we had hoped to find in our elliptical galaxy sample. NGC 4258 is a good analog because both it and the ellipticals are accreting at very low fractions of their Eddington luminosity (Ho 2008). In fact, given the typical observed luminosities, and inferred BH masses of $\sim {10}^{8}$ ${M}_{\odot }$, we do expect typical Eddington ratios of $\sim {10}^{-4}$, as in NGC 4258 (Herrnstein et al. 2005).

We can imagine scaling the properties of the NGC 4258 maser disk to infer the likely properties of comparable molecular disks around elliptical galaxies. If ${R}_{\mathrm{cr}}\propto {L}_{X}$ (as shown by Kondratko et al. 2006a) then, provided that the Eddington fraction, accretion efficiency, and the X-ray-to-bolometric efficiency stay roughly constant (likely a valid assumption, e.g., Vasudevan & Fabian 2007), we find that ${R}_{\mathrm{cr}}\propto {M}_{{\rm{BH}}}$. That is, the size of the accretion disk would scale linearly with the BH mass. In our sample, we expect the BHs are roughly an order of magnitude more massive than the BH in NGC 4258. Therefore, if this scaling roughly holds, their molecular disks would have sizes of ∼5–10 pc.

This scaling between X-ray luminosity, BH mass, and Eddington ratio introduces a possible explanation for the low incidence of megamaser disks in local elliptical galaxies. Because of the uniformly low Eddington ratio and high ${M}_{\mathrm{BH}}$, the accretion disk size will naturally grow by at least an order of magnitude. Likewise the Toomre (1964) Q parameter would decrease by a full order of magnitude at constant disk surface density, as Q depends linearly on the orbital frequency, and so inversely on R. It is not clear that accretion disks would be stable at a radius of 10 pc. Thus, one possible explanation for the lack of masers is that at high ${M}_{\mathrm{BH}}$ and low Eddington fraction, it is no longer physically possible to maintain a molecular disk with conditions appropriate for masing.

In actuality, the Eddington fraction in the ellipticals may be even lower than in NGC 4258. In the Palomar spectroscopic survey of galaxies, Ho (2008) finds that LINERs radiate at typical Eddington fractions of $\sim {10}^{-5}$, but span a large range from ${10}^{-7}$ to ${10}^{-3}$. If the Eddington ratio drops systematically toward more massive systems, the situation is more complicated than outlined in the previous paragraph and the disk size would not grow as rapidly with BH mass.

Another possibility is that the elliptical galaxy environment is less conducive to supporting molecular disks, even at a fixed Eddington fraction. Higher mass galaxies do host more hot X-ray gas, which could inhibit the formation of large amounts of dense molecular gas (Wiklind & Henkel 2001; O'Sullivan et al. 2001; Sarzi et al. 2006). Albeit on much larger scales, there are documented differences in the properties of molecular disks in elliptical and spiral galaxies. Davis et al. (2014) find that the molecular disks in early-type galaxies have star formation rates far below those expected from the Schmidt–Kennicutt relation (e.g., Kennicutt 1998). Their explanation is that the high levels of shear in the inner disk suppresses star formation. The maser disks are even deeper in the potential well, and we speculate that the gravitational potential may lead to a suppression of masing.

Even if we do not detect any masing disks, given our sample size we might have expected to detect megamasers associated with jet activity. As is well-documented in the literature, jets grow more prevalent in massive elliptical galaxies (e.g., Matthews et al. 1964; Best et al. 2005; Mandelbaum et al. 2009) and a high fraction of elliptical galaxy nuclei contain low levels of radio emission (e.g., Sadler et al. 1989; Wrobel & Heeschen 1991). Furthermore, elliptical galaxies with radio sources are also more likely to contain dust lanes (e.g., van Dokkum & Franx 1995) and dust is usually accompanied with molecular gas, which is needed to form or fuel the masing disk. Given the rising frequency of jet emission in elliptical galaxies, and particularly in the most luminous of elliptical galaxies, our non-detections are particularly interesting.

Here we might again invoke luminosity. Certainly jet power is known to correlate with [O iii] luminosity (e.g., Ho & Peng 2001). Another culprit is the lower gas mass in the elliptical galaxy. It is possible that because there is less molecular gas along the path of the jet, there are fewer opportunities for masing. Another factor is the geometry of the jet, as the Doppler-boosted forward jet may lie in front of the bulk of the molecular gas (see also Henkel et al. 1998).

As mentioned above, one of our primary motivations in embarking on this survey was to study the reliability of stellar dynamical BH masses (e.g., Gebhardt et al. 2003) via comparison with the BH mass derived from a megamaser disk. Precious few galaxies today have BH mass measurements based on multiple techniques (e.g., Siopis et al. 2009; Walsh et al. 2013), and even one such comparison in a massive elliptical would be extremely important.

Megamaser disks provide some of the only robust and unbiased measurements of ${M}_{\mathrm{BH}}$ in spiral galaxies. We have thus used these systems to measure scaling relations in late-type spiral galaxies that can be studied in detail with stellar dynamics. We see no compelling correlations between BH mass and galaxy properties in this regime (e.g., Greene et al. 2010; Sun et al. 2013).

Thus far, known megamaser disks are found orbiting AGNs with BH masses that are clustered around $\sim {10}^{7}$ ${M}_{\odot }$ (Herrnstein et al. 2005; Kuo et al. 2011) and mostly found in massive spiral galaxies (Greene et al. 2010). This narrow range in properties is likely a natural biproduct of the selection technique. In general, megamaser searches have focused on known active galaxies (e.g., Braatz et al. 1997; Kondratko et al. 2006b; Greenhill et al. 2009), predominantly selected based on their location in optical diagnostic diagrams (Baldwin et al. 1981; Veilleux & Osterbrock 1987). Since the typical obscured active galaxy in optically selected samples has ${M}_{\mathrm{BH}}$ $\sim {10}^{7}$ ${M}_{\odot }$ (Heckman et al. 2004; Greene & Ho 2007), it is not surprising that the majority of the discovered megamaser disk galaxies also have similar BH masses. At higher BH masses, the BHs are no longer highly active and thus are not included in the Seyfert galaxy catalogs. At lower BH masses, the dearth of sources is a selection effect due to (a) the difficulties of isolating accretion signatures in the presence of dust and star formation and (b) the fact that low-mass BHs are faint even when radiating at their Eddington limit (e.g., Greene & Ho 2007; Reines et al. 2013).

Having failed to find a megamaser disk around an ${M}_{\mathrm{BH}}$ $\gt {10}^{7}$ ${M}_{\odot }$ SMBH, we wish here to make a slightly different point about the potential biases inherent in stellar dynamical BH mass measurements (e.g., Gültekin et al. 2011). In principle, megamaser disks in massive elliptical galaxies have the potential to reveal a population of BHs that cannot be found using stellar dynamics. If the BH mass to galaxy mass ratio is small enough, then there will be no "gravitational sphere of influence" where the BH mass dominates the stellar dynamics. There will be no kinematic signature of the BH on the stars. On the other hand, a sub-parsec scale megamaser disk could still be within the sphere of influence of the BH, and thus probe the (hitherto unexplored) regime of very low ${M}_{\mathrm{BH}}$/${M}_{{\rm{gal}}}$.

In closing, we re-emphasize the importance of megamaser disks in revealing BH demographics at low mass. At low ${\sigma }_{*}$ in particular, there are not many remaining galaxies in the universe where we should be able to resolve the gravitational sphere of influence with present-day technology (assuming that ${\sigma }_{*}$ is a valid proxy; Batcheldor 2010; Gültekin et al. 2011; van den Bosch et al. 2015, their Figure 10), and at larger dispersion and luminosities, the situation is only a little better. Even with new facilities like JWST, ALMA (Davis 2014), and ELTs (Do et al. 2014), the improvement in spatial resolution will only probe one order of magnitude smaller in BH mass at a fixed galaxy property, which will not allow us to probe the full range in BH mass at ${\sigma }_{*}\lt 200$ km s⁻¹. Hence, even in the coming decades, masing disks and indirect AGN methods will remain critical for finding low-mass BHs (Reines & Volonteri 2015).