Atomic Clocks in Space: A Search for Rubidium and Cesium Masers in M- and L-Dwarfs
aa r X i v : . [ a s t r o - ph . S R ] J a n Draft version February 1, 2021
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Atomic Clocks in Space: A Search for Rubidium and Cesium Masers in M- andL-Dwarfs
Jeremy Darling Center for Astrophysics and Space AstronomyDepartment of Astrophysical and Planetary SciencesUniversity of Colorado, 389 UCBBoulder, CO 80309-0389, USA
ABSTRACTI searched for the ground state 6.8 and 9.2 GHz hyperfine transitions of rubidium and cesium towardM- and L-dwarfs that show Rb and Cs optical resonance lines. The optical lines can pump thehyperfine transitions, potentially forming masers. These spin-flip transitions of Rb and Cs are theprincipal transitions used in atomic clocks (the
Cs hyperfine transition defines the second). If theyare detected in stellar atmospheres, these transitions would provide exceptionally precise clocks thatcan be used as accelerometers, as exoplanet detectors, as probes of the predictions of general relativity,as probes of light propagation effects, and as a means to do fundamental physics with telescopes.Observations of 21 M- and L-dwarfs, however, show no evidence for Rb or Cs maser action, and aprevious survey of giant stars made no Rb maser detections.A RUBIDIUM AND CESIUM PRIMERRubidium has atomic number 37 and two common isotopes: Rb (stable) and Rb (49 Gyr half-life); the terrestrialisotopic ratio is 72:28 (Pringle & Moynier 2017). The Rb ground state hyperfine transition at 6.83468261090429(9)GHz (Bize et al. 1999) can form a maser and is often used as an atomic clock. Rb has one valence electron in the5 S / ground state, and the primary optical resonance transitions are 5 S / → P / and 5 S / → P / at 795and 780 nm. The 6.8 GHz Rb atomic clock maser relies on the hyperfine structure of the Rb optical resonancelines to selectively filter and optically pump the Rb hyperfine ground states, creating a population inversion andpromoting maser action (Bender et al. 1958; Davidovits & Novick 1966). The same processes may occur in stellar andsub-stellar atmospheres, producing a natural 6.8 GHz Rb maser.The analogous hyperfine cesium transition occurs at exactly 9.192631770 GHz; this transition defines the second.Unlike Rb, there is only one stable isotope of Cs,
Cs. The optical resonance lines at 852.3 and 894.6 nm correspondto the transitions 6 S / → P / and 6 S / → P / . The pumping of coherent 9.2 GHz Cs emission occurs viacollisions with buffer gases of similar pressure to that found in stellar photospheres, seems to be fairly independent ofbuffer gas species, and increases with temperature (Vanier et al. 1998). Laboratory work was limited by temperatureand did not include ions (although this is not an issue for M- and L-dwarf atmospheres), so the expectation for stellarCs maser action is less certain than it is for Rb (but still favorable).Astrophysical maser action requires the population inversion of a metastable state, seed photons to amplify (eithercontinuum or spontaneous emission in the maser transition), and a velocity-coherent amplification pathway. Theseprocesses can obtain in stellar atmospheres, which can be prodigious emitters of molecular masers such as SiO, OH,and H O (typically AGB stars). I predict that the conditions in stellar and sub-stellar atmospheres are promising for6.8 GHz Rb and 9.2 GHz
Cs maser action. The Rb I optical pumping lines have been observed in stellar andbrown dwarf atmospheres (e.g., Reiners et al. 2007). Cs is usually detected when Rb is detected, and the Cs maser iscollisionally pumped. Corresponding author: Jeremy [email protected] http://steck.us/alkalidata/ SCIENCE WITH CLOCKSPulsars have been used as cosmic clocks with great success (e.g., Backer & Hellings 1986; Burke-Spolaor 2015);detection and subsequent development of Rb and/or Cs masers would provide clocks in new classes of celestial objects.By tying terrestrial standards to clocks in space, one can test basic physics using telescopes, make (weak) tests ofgeneral relativity, detect exoplanets via Doppler wobble with unprecedented sensitivity, and, in concert with
Gaia proper motions, obtain precise three-dimensional kinematics of stars.It is worth stressing that all spectral lines are clocks. The power of Rb or Cs hyperfine transitions would lie in theirradio frequency maser action, which enables extremely precise Doppler tracking and astrometry compared to any UV,optical, or IR transitions (no bright radio emission lines are known in main sequence stars or brown dwarfs).ASTROPHYSICAL RUBIDIUM AND CESIUMThe optical resonance lines of alkali metals including Rb I and Cs I have been detected in main sequence stars, browndwarfs (Manjavacas et al. 2016), giant stars (e.g., Garc´ıa-Hern´andez et al. 2006), and even a candidate Thorne- ˙Zytkowobject in the Small Magellanic Cloud (Levesque et al. 2014). The Rb and Rb lines are blended and cannot bedistinguished in optical spectra, but the observed presence of other s-process elements, such as Zr, can be used to inferthe presence of Rb when the blended Rb I lines are detected.Despite the lower abundance of Cs compared to Rb (Lodders 2003), Cs absorption lines can be optically thick.Velocity-coherent column density is key for maser action, and stellar atmospheres satisfy this requirement; the questionfor maser production is whether the pumping of Rb or
Cs is quenched by collisions. It is worth noting that masershave almost always been discovered rather than predicted; they amplify small-scale physical conditions that may notbe representative of the bulk properties of a gas. Addressing the possibility of Rb or Cs masers in stellar atmospherestherefore requires observations. A small Green Bank Telescope survey of giant stars found no 6.8 GHz Rb emission(Darling 2018), so I turn to low-mass stars and brown dwarfs, which provide less distance-dimming and more practicalscientific applications for maser lines, including exoplanet detection and characterization.OBSERVATIONSI selected a sample of 13 M-dwarfs and 8 L-dwarfs where Rb I and Cs I are prominent in SDSS DR16 optical spectra(Ahumada et al. 2020), indicating these elements are abundant and that the maser pumping lines are optically thick.Using the NSF’s Karl G. Jansky Very Large Array (VLA), I searched for the 6.8 GHz Rb and 9.2 GHz
Cslines. VLA observations used the C configuration with integration times of ∼
10 min, 3 s sampling, and dual circularpolarizations. Bandpasses with 3.91 kHz (0.17 km s − ) channels spanning 8 MHz (351 km s − ) were centered on the6.83468261 GHz Rb, and 6.66852 GHz CH OH transitions, appropriately Doppler shifted to the velocity of eachtarget. The 9.19263177 GHz Cs observations used 5.208 kHz (0.17 km s − ) channels spanning 16 MHz (522 km s − ).Synthesized beams ranged from 2.6 ′′ × ′′ to 7.3 ′′ × ′′ . I used CASA (McMullin et al. 2007) for interferometricflagging, calibration, and imaging. Spectral cubes were polarization-averaged and smoothed to 1 km s − to achieve2 mJy rms noise. No continuum was subtracted from the cubes.RESULTS AND CONCLUSIONSI searched for emission features over a broad velocity range ( ±
125 km s − ), taking into account the sometimes highproper motions of the targets. No credible maser features were identified. Table 1 lists the targets, SDSS spectra, andthe rms noise of the non-detected transitions.These results suggest that Rb and Cs masers are unlikely to occur frequently in M- and L-dwarf atmospheres. Asurvey of 10 giant stars and two globular clusters for the 6.8 GHz Rb maser by Darling (2018) likewise made nodetections. I suggest that the search should continue, perhaps toward other types of stars and in the interstellarmedium.I thank Z. Berta-Thompson for help with astrometry.
Facilities:
VLA
Software:
CASA (McMullin et al. 2007) The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement byAssociated Universities, Inc.
Table 1.