SOFIA/GREAT Discovery of Terahertz Water Masers^∗

Maser action is widely observed in nature. It amplifies the emission from specific transitions of abundant astrophysical molecules in a variety of environments, including the interstellar medium, circumstellar envelopes, and the accretion disks within active galactic nuclei. Among the half-dozen astrophysical molecules that have been observed to exhibit the maser phenomemon, water vapor possesses the brightest known maser transitions, with brightness temperatures for its 22 GHz ${6}_{16}-{5}_{23}$ transition often exceeding 10¹⁰ K and in exceptional cases reaching 10¹⁴ K. Thanks to these extraordinarily high brightness temperatures, this transition can be observed by means of Very Long Baseline Interferometry, providing submilliarcsecond angular resolution that enables a variety of astronomical studies that have greatly expanded our understanding of the kinematics of protostellar outflows; helped elucidate the size, shape, and kinematics of the Milky Way (e.g., Reid et al. 2009); and have provided among the best evidence yet obtained for the existence of supermassive black holes (e.g., Miyoshi et al. 1995).

In the decades following the first detection of interstellar water vapor through its masing 22 GHz transition (Cheung et al. 1969), additional water maser transitions have been discovered at higher frequencies. In Table 1, we provide a list of all observed maser transitions within the ground vibrational state of water that have been detected at high spectral resolution with the use of heterodyne receivers. NASA's airborne astronomy program played an early role in these discoveries, with the first detections of the 183 GHz (Waters et al. 1980) and 380 GHz (Phillips et al. 1980) transitions having been obtained using the Kuiper Airborne Observatory. In the 1990s and 2000s, thanks to the development of heterodyne receivers on ground-based submillimeter telescopes at dry, high-altitude sites, several additional maser transitions were detected in the 300–500 GHz range. More recently, two additional water maser lines—at frequencies in the 500–1000 GHz range—were detected using the HIFI instrument on Herschel. These transitions are indicated in the energy level diagram shown in Figure 1.

Zoom In Zoom Out Reset image size

Table 1.  Observed Maser Transitions within the Ground Vibrational State of Water

Transition	Frequency	EU/ka	Discovery	Environment(s)b
	(GHz)	(K)	Reference
616 − 523	22.235	644	Cheung et al. (1969)	IS, CSE, AGN
${3}_{13}-{2}_{20}$	183.310	205	Waters et al. (1980)	IS, CSE, AGN
${4}_{14}-{3}_{21}$	380.197	323	Phillips et al. (1980)	IS
${10}_{29}-{9}_{36}$	321.226	1861	Menten et al. (1990a)	IS, CSE, AGN
${5}_{15}-{4}_{22}$	325.153	575	Menten et al. (1990b)	IS, CSE
${7}_{53}-{6}_{60}$	437.347	1525	Melnick et al. (1993)	CSE
${6}_{43}-{5}_{50}$	439.151	1089	Melnick et al. (1993)	IS, CSE
${6}_{42}-{5}_{51}$	470.889	1090	Melnick et al. (1993)	IS, CSE
${5}_{33}-{4}_{40}$	474.689	725	Menten et al. (2008)	CSE, IS
${5}_{32}-{4}_{41}$	620.701	732	Harwit et al. (2010)	IS, CSE
${5}_{24}-{4}_{31}$	970.315	599	Justtanont et al. (2012)	CSE
${7}_{43}-{6}_{52}$	1278.266	1340	present work	CSE
${8}_{27}-{7}_{34}$	1296.411	1274	present work	CSE
${8}_{45}-{7}_{52}$	1884.888	1615	present work	CSE

Notes.

^aEnergy of the upper state (temperature units) relative to the ground state of para-H₂O. ^bIS—interstellar; CSE—circumstellar envelopes; AGN—active galactic nuclei.

Download table as:  ASCIITypeset image

Multitransition maser observations provide key constraints on the pumping mechanisms that lead to a population inversion and on the physical conditions in the masing region (Neufeld & Melnick 1991; hereafter NM91). All the masing transitions shown in Figure 1 have ΔJ = −1 and ΔK_A = +1, a behavior predicted by models that invoke a combination of collisional excitation and spontaneous radiative decay as the origin of the population inversion. Although the quantitative predictions of such models do depend upon the details of the collisional rate coefficients, the question of which transitions become inverted is largely determined by the arrangement of the energy levels (e.g., NM91). Specific transitions become inverted because the upper state has a longer lifetime than the lower state for radiative decay via non-masing far-infrared transitions. Any population inversion inevitably involves a departure from local thermodynamic equilibrium, and the magnitude of the required departure is an increasing function of the transition frequency, as are the spontaneous radiative decay rates for the masing transition. These considerations raise the following questions: what is the maximum frequency of water transitions in which a population inversion can occur in astrophysical environments? Furthermore, even if a population inversion is present, at what point does spontaneous radiative decay dominate stimulated emission?

To address these questions, to test the collisional pumping scheme proposed as the origin of water maser emission, and to probe the physical and chemical conditions within circumstellar envelopes, we used the GREAT instrument on SOFIA to search for Terahertz maser transitions toward four oxygen-rich evolved stars: W Hya, U Her, R Aql, and VY CMa. The target sources have all been known to exhibit water maser emission in multiple lower-frequency transitions (e.g., Menten & Melnick 1991). The primary transition of interest was the 8₂₇ − 7₃₄ line at 1.296 THz, a transition predicted to be strongly masing (NM91; Gray et al. 2016); in addition, we targeted the ${8}_{45}-{7}_{52}$ line at 1.885 THz toward all four sources at the same time as the 1.296 THz line, and the ${7}_{43}-{6}_{52}$ line at 1.278 THz toward VY CMa. The observing strategy and data reduction methods are described in Section 2 below, and the results presented in Section 3. In Section 4, we discuss the results in the context of models for water maser emission from the circumstellar envelopes of evolved stars.

Table 2 lists the evolved stars toward which the water transitions were observed, along with the positions targeted, the estimated distance to each source, the period of the stellar variability, the spectral type, the source systemic velocity relative to the local standard of rest (LSR), and the estimated mass-loss rate. Also shown are the date of each SOFIA observation, the corresponding stellar phase, the velocity of Earth's atmosphere relative to the LSR, the observatory altitude at the time of the observation, and the total integration time.

Table 2.  Source Parameters, Observational Parameters, and Observed Line Parameters

Source:	W Hya	U Her	R Aql	VY CMa
Source parameters
R.A. (J2000)	13h 49m 0199	16h 25m 4747	19h 06m 2225	07h 22m 5833
Decl. (J2000)	−28° 22' 035	+18° 53' 329	+08° 13' 469	−25° 46' 032
Distance (pc)	78 ± 6a (K03b)	266 ± 30 (V07)	214 ± 39 (K10)	1200 ± 115 (Z12)
Variability periodc (days)	361	406	270	956
Systemic velocityd (km s−1)	40.0 ± 0.5	−13.4 ± 0.8	48.7 ± 0.8	17.6 ± 1.5
Spectral typec	M7.5e-M9ep	M6.5e-M9.5e	M5e-M9IIIe	M5eIbp(C6,3)
Estimated mass-loss rate (10−6 M⊙ yr−1)	0.13 (K14)	2.6 (G71)	0.8 (G71)	150 (R10)
Observational parameters
Date of SOFIA observation	2016 May 27	2016 May 26	2016 Nov 10	2017 Feb 01
Stellar phasee	0.71	0.99	0.64	...
Date of Effelsberg observation	2016 May 11	2016 May 26	2016 Nov 14	2017 Feb 01
Source velocity relative to SOFIA (km s−1)	52	−31	53	41
Observatory altitude (kft)	43	40–41	39–40.5	42
SOFIA integration time (minute)f	11	14	14	23
Integrated line fluxes (Jy km s−1)
22 GHz	86.5	167	46	9300
1.278 THz	...	...	...	10500 ± 790
1.296 THz	6970 ± 330	1220 ± 170	<1120g	11220 ± 520
1.885 THz	3690 ± 530	550 ± 300	<1170g	11080 ± 660
Photon luminosities (1041 s−1)
22 GHz	3.17	71	12.6	80700
1278 GHz	...	...	...	91100 ± 6900
1296 GHz	255 ± 12	519 ± 73	<307g	97400 ± 4500
1885 GHz	135 ± 19	235 ± 128	<322g	96100 ± 5700
Photon luminosity ratios
22 GHz/ 1296 GHz	0.0124 ± 0.0006	0.137 ± 0.019	>0.041	0.829 ± 0.0038
Line centroids (km s−1 relative to the LSR)
22 GHz	38.7	−14.6	46.5	15.1
1.278 THz	...	...	...	19.7
1.296 THz	38.7	−15.4	...	19.6
1.885 THz	39.7	−16.3	...	22.6
Line velocity dispersions (in km s−1)
22 GHz	1.85	1.17	1.08	7.93
1.278 THz	...	...	...	10.95
1.296 THz	3.26	1.73	...	8.77
1.885 THz	3.66	1.68	...	8.12

Notes.

^aWhere given, errors are 1σ statistical errors. ^bReferences: K03—Knapp et al. (2003), V07—Vlemmings & van Langevelde (2007), K10—Kamohara et al. (2010), Z12—Zhang et al. (2012), K14—Khouri et al. (2014), G71—Gehrz & Woolf (1971), R10—Royer et al. (2010). ^cGeneral Catalog of Variable Stars, v5.1 (Samus' et al. 2017). ^dRelative to the LSR, as determined from observations of thermal SiO emission (Dickinson et al. 1978). ^eDetermined from recent visual light curves generated by AAVSO (www.aavso.org). ^fOn source integration time. ^g3σ upper limit obtained for the 43–52 km s⁻¹v_LSR range.

Download table as:  ASCIITypeset image

The 1.278 and 1.296 THz water lines were observed in the upper sideband of the L1 receiver of GREAT using the FFT4G backend; the latter provides ∼16,000 spectral channels with a spacing of 283 kHz. The 1.885 THz water line was observed simultaneously in the lower sideband of the LFA receiver. At frequencies of 1.296 and 1.885 THz, the telescope beam has a diameter of ∼20'' and ∼14'' (HPBW) respectively. The observations were performed in dual beam switch mode, with a chopper frequency of 1 Hz and the reference positions located 60'' on either side of the source along an east–west axis.

The raw SOFIA data were calibrated to the ${T}_{A}^{* }$ ("forward beam brightness temperature") scale, using an independent fit to the dry and the wet content of the atmospheric emission. Here, the assumed forward efficiency was 0.97 and the assumed main beam efficiency for the L1 band was 0.67. The uncertainty in the flux calibration is estimated to be ∼20% (Heyminck et al. 2012). Additional data reduction was performed using CLASS.⁶ This entailed the removal of a first-order baseline and the rebinning of the data to a channel width of 0.51 km s⁻¹ (1296 GHz line), 0.93 km s⁻¹ (1885 GHz line), or 1.03 km s⁻¹ (1278 GHz line).

We used the Effelsberg 100 m telescope to carry out observations of the 22.23508 GHz 6₁₆ − 5₂₃ transition toward all four sources. In all cases, these observations were performed within 16 days of the SOFIA observations, and for U Her and VY CMa they were carried out on the same day. The 22 GHz observations were performed with the new secondary focus receiver, with a beam size of 41'' (HPBW), which was connected to an FPGA-based FFT spectrometer providing a frequency resolution of 1.5 kHz. The data were calibrated by correcting for atmospheric opacity and the dependence of the telescope gain on elevation. For the conversion of the observed spectra into jansky, suitable calibration sources like 3C 286, NGC 7027, etc., were observed to determine the telescope's sensitivity (which was about 1 K Jy⁻¹ for all observations).

In Figure 2, we present the reduced spectra obtained from both SOFIA and Effelsberg for all four sources. The 22 GHz line was observed at a very high signal-to-noise ratio in all sources, and the 1.296 THz line was unequivocally detected toward all sources except R Aql. The 1.885 THz line was clearly detected toward W Hya and VY CMa. A search for the 1.278 THz line was only conducted toward one source, VY CMa, and led to a clear detection. The 1.278 and 1.296 THz H₂O lines had previously been detected toward VY CMa in spectrally unresolved observations reported by Matsuura et al. (2014) using the SPIRE instrument on Herschel. In Table 2, we present the line-integrated fluxes measured for each source, as well as the velocity centroids and velocity dispersions for cases in which a line was detected.

Zoom In Zoom Out Reset image size

4.1. Maser Line Ratios

4.2. Simple Model for W Hya

While the detailed modeling of the observed water maser emissions is beyond the scope of this paper, we present a simplified model for one of the sources, W Hya. Here, we adopted the gas temperature and velocity profiles given by Khouri et al. (2014), and used the excitation model described above to compute the following quantities for each transition as a function of distance from the star: the maser optical depth along a tangential ray in the unsaturated limit, τ(unsat); the photon emission rate per unit volume in the limit of saturation, Φ_p(sat); and the rate of spontaneous radiative decay per unit volume Φ_p(spont). These quantities were computed with the use of the Large Velocity Gradient (LVG) approximation. In the top left panel of Figure 3, the gas temperature and radial outflow velocity are shown by black and blue curves as a function of distance, R, from the center of the star. The other three panels, labeled by transition frequency, show 4πR³Φ_p(sat) (black) and 4πR³Φ_p(spont) (red) for each transition. Presented in this format, with the volumetric emission rates multiplied by 4πR³, these curves show the photon luminosity per logarithmic radial interval.

Zoom In Zoom Out Reset image size

In regions where a population inversion is present (τ(unsat) < 0), the total photon emission Φ_p is bracketed by Φ_p(sat) and Φ_p(spont). For the 22 GHz transition, Φ_p(sat) typically exceeds Φ_p(spont) by a factor ∼10⁶, and a very large maser gain would be needed to achieve saturation. For the two THz maser transitions, Φ_p(sat) exceeds Φ_p(spont) by at most a factor 10, and only a relatively small gain is needed to achieve saturation. In our simple model, we estimate the actual photon emission rate, Φ_p, by considering maser amplification along tangential rays, assuming that maser amplifies seed radiation consisting of (1) the cosmic microwave background radiation and (2) radiation emitted by the spontaneous radiative decay. With these assumptions, we may obtain line flux predictions for all three transitions. The best agreement with the observed line fluxes, with all three line flux predictions within 15% of the observed values, was obtained for an assumed mass-loss rate of $\dot{M}=7\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ and an ortho-water abundance of $x({\rm{o}}-{{\rm{H}}}_{2}{\rm{O}})=3.1\times {10}^{-4}$ relative to H₂. The resultant gas density profile is shown by the red curve in the top left panel of Figure 3, and the actual rate of photon emission is shown by the blue curves in the other three panels. Clearly, for the THz frequency transitions, the predicted line emission is very close to the maximum achievable for saturated masers. For the 22 GHz transition, however, the emission is unsaturated. In this case, the predicted line luminosity depends very sensitively upon $\dot{M}$, $x({\rm{o}}-{{\rm{H}}}_{2}{\rm{O}})$ and the details of the velocity field.

The best-fit values we obtained for both $\dot{M}$ and $x({{\rm{H}}}_{2}{\rm{O}})$ are roughly a factor two below the best-fit estimates obtained by Khouri et al. (2014) from a fit to non-masing water transitions. This discrepancy is perhaps unsurprising given the simple nature of the model. A more detailed treatment would require the use of a detailed radiative transfer model for the maser radiation and the stellar and dust continuum radiation, with full inclusion of radiative pumping in rotational and rovibrational lines. Moreover, because the radial velocity gradient is zero within the region interior to the acceleration zone, an accurate calculation would require a treatment beyond the standard LVG approximation.

4.3. Relative Importance of Stimulated Emission

Based on observations made with the NASA/DLR Stratospheric Observatory for Infrared Astronomy, and the 100 m radio telescope of the MPIfR in Effelsberg. SOFIA Science Mission Operations are conducted jointly by the Universities Space Research Association, Inc., under NASA contract NAS2-97001, and the Deutsches SOFIA Institut under DLR contract 50 OK 0901. This research was supported by USRA through a grant for SOFIA Program 04-0023. We gratefully acknowledge the outstanding support provided by the SOFIA Operations Team and the GREAT Instrument Team.