Megamaser Cosmology Project II : The prospects for measuring a 1% Ho and distances to high-z galaxies

Abstract H2O megamaser emission from sub-parsec circumnuclear disks at the center of active galaxies allows a single-step, direct distance measurements to galaxies in the Hubble flow without any external calibration. Based on accurate distance determinations of six maser galaxies within 150 Mpc, the Megamaser Cosmology Project (MCP) team recently obtained H0 = 73.9± 3.0 km/s/Mpc (‘∼ 4% accuracy), independent of distance ladders and the cosmic microwave background. To further applying the megamaser technique to attain a 1% Ho measurement, detecting more high-quality disk maser systems is crucial. In this conference proceeding, we update the status of the MCP and discuss strategies of detecting additional high-quality disk maser galaxies within z ∼ 0.1. In addition, we show the prospects of reaching a 1% Ho measurement with the supreme sensitivity of the ngVLA. Finally, we demonstrate that applying the maser technique to distance measurements of high-z galaxies with future submm VLBI systems is promising and this will allow for investigation of the new tension between the ΛCDM model and the high-z Hubble diagram.


Introduction
Astrophysical water masers are natural microwave amplifiers by stimulated emission of radiation.Observations in the past three decades have shown that maser emissions from the 6 16 − 5 23 transition of ortho-H 2 O at 22.23508 GHz are abundant in star-forming regions and in the nuclear regions of some galaxies hosting active galactic nuclei (AGNs).When detected at galaxy centers, the 22 GHz H 2 O masers are typically millions of times more luminous than those associated with typical star-forming regions in the Milky Way galaxy.They are therefore termed "megamasers." H 2 O megamasers provide a direct determination of the Hubble Constant, H 0 , independent of standard candles (Reid et al. 2013), and enable precise measurements of supermassive black hole (BH) masses, M BH (Gao et al. 2017), via sub-milliarcsecond imaging of H 2 O maser emission from disk maser systems, such as NGC 4258 (see Figure 1; Herrnstein et al. 1999;Argon et al. 2007).In such a system, the masing gas resides in a subparsec-scale thin disk viewed almost edge-on and following near Keplerian rotation.These disk properties support M BH measurements to percent-level accuracy (Kormendy & Ho 2013), and the disk maser geometrical and kinematic information can be modeled to provide a standard ruler for measuring an accurate angular-diameter distance to a galaxy well into the Hubble flow (Kuo et al. 2013) without relying on distance ladders and the cosmic microwave background (CMB).
To resolve the Hubble tension, numerous models (i.e.>30) have been proposed to modify or replace the ΛCDM model, such as dynamical dark energy, early dark energy, phantom crossing, and modified theory of gravity (see a thorough review in Di Valentino et al. 2021).Many of these models have been shown to resolve the Hubble tension if one only uses CMB data for modeling.However, when Baryon Acoustic Oscillation (BAO) data is included in the analysis, tension is restored for some models (e.g.Yang et al. 2021), making these models less favorable.This suggests that more cosmological datasets from various different probes are needed to break degeneracies between models (King et al. 2014) and to identify the best solutions that could resolve the Hubble tension.

The Need for New High-z Distance Indicator
In recent years, accurate measurements of distances to high-z galaxies have been proposed as an important probe that could break degeneracies between cosmological models.To demonstrate an example, King et al. (2014) show that the differences between distance moduli predicted from the standard ΛCDM and various models of dynamical dark energy are large enough to be distinguishable only at z > ∼ 1, which is probed only by a small fraction of Type Ia supernovae.One needs new distance indicators beyond z∼1 to differentiate between the dynamical dark energy and ΛCDM models.
To reach the high-z universe, Lusso et al. (2019) use luminous quasars as new standard candles for measuring galaxy distances up to z∼5 based on the quasar X-ray/ultraviolet luminosity correlation.Their work shows that the best fit to the high-z Hubble diagram indicates a ∼4σ deviation from the ΛCDM prediction (see Figure 2), suggesting a tension with the standard model at high redshifts.However, recent studies argue that the quasar luminosity correlation is redshift-dependent, and the ∼4σ deviation seen in Lusso et al. (2019) could be a result of redshift evolution of quasar properties (e.g.Li et al. 2022).To avoid the impact of galaxy evolution on distance measurements, we need an alternative tool such as the H 2 O maser technique, which is based on well-known gas dynamics and does not suffer from the redshift-dependent effects.When applied to high-z galaxies, this technique is promising to provide substantially more accurate distance measurements than the quasar method.In addition, it will enable direct, dynamical measurements of BH masses at z > ∼ 1 for the first time, enhancing studies of the black hole/host-galaxy coevolution (Kormendy & Ho 2013) in the early universe.

The Importance of Improving the Hubble Constant Measurements
While resolving the Hubble tension may require new cosmological probes of the high-z universe, continuing to improve the accuracy of the Hubble constant is equally important.The long-term goal of the observational cosmology community is to attain a 1% H 0 measurement with agreement across multiple, independent observational approaches, including the H 2 O megamaser technique.Having an H 0 with such an accuracy would be essential to check whether the current discrepancy in different H 0 measurements could partly or entirely result from unrecognized systematic uncertainties in underlying observations.In addition, it can provide the theoretical community a more precise determination of the difference between H 0 obtained from direct and indirect methods, giving a tighter constraints on various models of cosmology.It is likely that future joint analysis of cosmological datasets that include a 1% H 0 and accurate distances to high-z galaxies could substantially deepen our understanding of the Hubble tension problem.

The 2nd Phase of the Megamaser Cosmology Project : MCPII
To fully harness the potential of using the H 2 O megamaser technique for studying cosmology, we attempt to apply the maser technique to both low-z and high-z galaxies in the next stage of the Megamaser Cosmology Project (MCPII).In the "low-z MCPII" project, we continue to use the H 2 O megamaser technique to measure accurate distances to additional maser galaxies at low redshifts (i.e.z < ∼ 0.1) to achieve a ∼1% H 0 .For the "high-z MCPII", we aim to apply the H 2 O megamaser technique to high-z galaxies and use their maser-based distances as a new cosmological probe to identify the origin of the Hubble tension.The details of the two aspects of the MCPII are described as follows:

Accurate H 0 measurements with the ngVLA at Low Redshifts
From the latest H 0 determination from (Pesce et al. 2020), the current accuracy of H 0 achieved with the H 2 O maser technique is ∼4%.To improve the accuracy from ∼4% to ∼1%, we need accurate distances (i.e.accuracy ∼ 7%) to additional 50 maser galaxies (Braatz et al. 2019).Before making new distance measurements for additional galaxies, it is essential to first looking for new, high-quality disk maser galaxies within z ∼ 0.1 with improved survey strategy.The number of disk maser systems that have been found by previous single-dish H 2 O maser surveys is > ∼ 30, insufficient for a 1% H 0 measurement.To find out additional >20 new disk megamasers, a blind survey on all Seyfert 2 galaxies and Liners as done in the MCP is no longer practical because the detection rate of disk megamasers is found to be only ∼1% based on this survey strategy.To improve the detection rate of disk maser systems, Kuo et al. (2020) found that it is easiest to find disk masers if a survey targets Compton-thick (CT) AGNs (i.e.column density of X-ray obscuring medium N H > ∼ 10 24 cm −2 ).As shown in Figure 4, the detection rate of disk masers reach ∼20% if an AGN has N H ≥ 10 24 cm −2 .In contrast, the disk maser detection rate drops rapidly when N H < 10 24 cm −2 .This suggests that targeting Compton-thick AGNs can boost the disk maser detection rate by a factor of ∼20, allowing one to identify the required number of disk megamasers by surveying a much smaller sample of galaxies.
In addition to searching for additional disk maser systems with new survey strategy, improving the sensitivity of current Very Long Baseline Interferometry (VLBI) facilities is also critical.Among the ∼30 disk megamasers that have been discovered, only ∼10 have sufficiently strong maser lines and the required spectral characteristics † for accurate † An accurate distance measurement with the H2O megamaser method requires detections of multiple blueshifted and redshifted maser features to accurately characterize the Keplerian rotation curve of a disk maser system.In addition, the systemic masers also need to be strong enough for precise acceleration measurements (e.g.Kuo et al. 2015).distance measurements.For the rest of ∼20 disk maser systems (see Figure 3; Pesce et al. 2015), the maser emissions are too faint to enable accurate distance measurements.To measure accurate distances to these maser galaxies, the sensitivity of current VLBI facilities needs to be improved significantly.This will be realized soon with the advent of the next-generation Very Large Array (ngVLA), which would bring about an order of magnitude improvement in sensitivity.The enhanced sensitivity of the ngVLA will not only allow for efficient detections of maser systems in a ∼30 times larger volume, it will also permit accurate distance measurements for the fainter disk maser systems, making a 1% H 0 determination possible with the maser technique in the future.

Reaching the High-z Universe with Submillimeter H 2 O Gigamaser Emissions
Based on a relatively recent modeling of H 2 O maser emissions (Gray et al. 2016), it has been shown that some of submillimeter H 2 O maser lines can be significantly stronger than the well-known 22 GHz water maser, suggesting that submillimeter water masers may be a better tool to access the high-z universe than the 22 GHz maser given the availability of Atacama Large Millimeter/submillimeter Array (ALMA).Among the most luminous submillimeter water masers that could be present in the circumnuclear gas disks in high-z galaxies, the H 2 O maser emissions 4 14 − 3 21 at 380.19736 GHz is one of the most promising lines that would allow for distance measurements of high-z galaxies.The 380 GHz transition corresponds to the back-bones levels, i.e. levels with the lowest energy for a given rotational quantum number (e.g. de Jong 1973).Members of the back-bone group are expected to display large line strengths resulting in large optical depths, slowing down radiative decay and thus carrying the bulk of the population.Based on modelling done by (Gray et al. 2016), the 380 GHz maser transition can be intrinsically brighter than the 22 GHz water maser line by a factor of > ∼ 10 under certain physical conditions, making high signal-to-noise detections of high-z maser emissions possible.
Despite the line strength of the 380 GHz maser could be significantly higher than that of the 22 GHz H 2 O maser, its frequency falls into a deep absorption trough in the Earth's atmosphere.As a result, it can only be observed from space if the maser emission is from a source in the local universe.However, since we are targeting high-z galaxies, the 380 GHz lines are redshifted to frequency bands that can be easily accessible for follow-up by existing VLBI facilities, which can provide extremely high resolution maser mapping (e.g.∼20−40 μas).Based on our recent model prediction of the angular sizes of H 2 O maser disks at z > 1 (i.e.∼3.4 mas or ∼30 pc in physical size; Kuo et al. in prep.), we infer that if > ∼ 5σ detections of the 380 GHz maser emissions can be achieved in future follow-up VLBI observations that include ALMA, the maser maps would have fractional uncertainties (i.e.maser position uncertainties < ∼ 10 μas) nearly as small as those in the maser disk in NGC 4258 (Figure 1), making highly accurate distance and BH mass measurements feasible at high redshifts.
The 380 GHz H 2 O maser line has been detected toward ∼10 starburst galaxies and 1 type-1 quasar at z > ∼ 2 in recent ALMA cycles (Yang et al. in prep.), but robust detections of disk maser systems have not yet been made.To optimize the chance of detecting disk maser systems, it is beneficial to first target Compton-thick quasars at z ∼ 2 (i.e. the peak of quasar space density) in future ALMA observations.One expects higher maser detection rates in these systems because the fraction of nearly edge-on disk masers is known to be highest in CT AGNs (see Figure 4; Kuo et al. 2020).In addition, a recent modeling of the physical conditions in disk maser systems (Kuo et al. in prep.)suggests that the maser amplification path length L amp for an edgeon maser disk is strongly correlated with BH mass.Given that the BH mass function of luminous quasars at z ∼ 2 peaks at M BH ∼ (1 − 3)×10 9 M (i.e.> ∼ 100 times more massive than BHs in local H 2 O megamasers; see Figure 5; Vestergaard & Osmer 2009), this model predicts that L amp for a quasar maser disk at z ∼ 2 would be significantly greater than that for a low-z disk maser, leading to a boost in maser intensity by a factor of > ∼ 100 for saturated masers.
Finally, since the 380 GHz maser transition could be intrinsically brighter than the 22 GHz water maser line by a factor of > ∼ 10 ( Gray et al. 2016), the total maser luminosity of the 380 GHz line of a quasar maser disk at z ∼ 2 is likely to be > ∼ 1000 times greater than that of a low-z 22 GHz water maser disk, making detections of high-z 380 GHz maser emissions possible without gravitational lensing.We can thus call these high-z 380 GHz water maser systems "Gigamasers".Depending redshifts (i.e.1.2 < z < 3.5; set by the spectral coverage of ALMA bands 3 through 5), the peak flux densities of the 380 GHz maser emissions from CT quasars are expected to be ∼1.5−4mJy, estimated based on the typical peak luminosity densities of the 22 GHz water maser lines L ν in the low-z disk megamaser systems (L ν ∼ (2 − 4) × 10 29 erg/s/Hz; see Figure 6) plus the expectation that the 380 GHz maser emissions from high-z quasar maser disks could be > ∼ 1000 stronger than the local 22 GHz maser disks.Given the sensitivities of ALMA, the 380 GHz lines of high-z CT quasars can be detected within integration times of ∼1−5 hours.
In the past two decades, deep X-ray observations of high-z galaxies have led to detections of more than 100 CT quasars at z > 1 (e.g.Lanzuisi et al. 2009;Gilli et al. 2022).Table 1 shows some CT quasars discovered by (Brightman et al. 2014).If our modeling of disk maser systems is correct, it is promising that ALMA will detect H 2 O gigamasers from the high redshift universe in the near future.

Conclusion
The studies of H 2 O disk megamaser systems in the past two decades have demonstrated that the H 2 O megamaser technique enables an accurate, robust determination of the Hubble constant and provide an important consistency check for H 0 values obtained across multiple, independent observational approaches.Comparisons of H 0 from different methods have clearly indicated a significant tension between direct measurements of H 0 and predictions based on the CMB assuming the ΛCDM model.To understand the origin of the Hubble tension problem, we have shown that achieving a 1% H 0 measurement is important.In addition, accurate distance measurements of high-z galaxies would be a new probe that could break degeneracies between models that could resolve the Hubble tension.For the purpose of improving the accuracy of H 0 and measuring precise distances to high-z galaxies, the H 2 O megamaser technique will play an important role in the future.At low redshifts, the supreme sensitivity of the ngVLA will allow for efficient detections of disk megamaser systems within z < ∼ 0.1 and enable accurate distance measurements for > ∼ 50 galaxies, making a 1% Hubble constant measurement possible.For the high redshift universe, we predict that some of the submillimeter H 2 O maser lines such as the 380 GHz   maser transitions from highly obscured quasars could be > ∼ 1000 times more luminous that local 22 GHz disk megamasers.This makes the detections of these systems possible with ALMA without strong gravitational lensing.The follow-up VLBI observations of these water "gigamasers" are promising to give maser maps that are as accurate as the prototypical maser system NGC 4258, making precise distance measurements of high-z galaxies feasible.By combining the low-z and high-z distance measurements, the H 2 O megamaser technique would provide a unique probe of the cosmic expansion history over a wide range of redshifts, permitting independent constraints on new models of cosmology.

Figure 1 .
Figure 1.The distribution and Keplerian rotation curve (Argon et al. 2007) of the 22 GHz H2O masers in NGC 4258.

Figure 2 .
Figure 2. Hubble diagram showing a distance modulus, μ, normalized to that expected for a ΛCDM universe.The yellow dots indicate distance measurements using the quasar technique (Lusso et al. 2019).

Figure 3 .
Figure3.The 22 GHz H2O maser spectra of nine disk maser systems discovered by the MCP(Pesce et al. 2015).These systems are a subset of the candidate disk megamasers in which the maser features are either too faint or the velocity ranges covered by the systemic masers are too narrow to allow for accurate distance measurements with the sensitivity of current VLBI facilities such as the High Sensitivity Array.

Figure 4 .
Figure 4. Detection rates of megamasers and disk masers as a function of column density NH (Kuo et al. 2020).

Figure 5 .
Figure 5.The BH masses distributions of luminous quasars obtained from Vestergaard & Kumar (2009).The left panel shows the BH mass as a function of redshift and the right panel shows the BH mass functions for various redshift bins.These figures show that at the redshift around z ∼ 2, the BH mass function peaks at MBH ∼ 10 9 M .

Figure 6 .
Figure 6.The luminosity densities Lν of the 22 GHz H2O maser emissions of eight edge-on disk maser systems discovered by the MCP(Kuo et al. in prep).The median luminosity densities of these systems, especially their redshifted and blueshifted maser components, are all around L ν ∼ 10 29 erg s −1 Hz −1 , suggesting that edge-on maser disks behave like standard candles.This property enables predictions of the flux densities of maser emissions from edge-on H2O maser disks at different redshifts.

Table 1 .
Compton-thick Quasars in the Chandra Deep Field South and the COSMOS field.