Astrophysical constraints on the proton-to-electron mass ratio with FAST
aa r X i v : . [ a s t r o - ph . I M ] A p r Research in Astronomy and Astrophysics manuscript no.(L A TEX: FASTissue˙chenxi˙v3.tex; printed on April 10, 2019; 0:27)
Astrophysical constraints on the proton-to-electron mass ratio withFAST
Xi Chen , , Simon P. Ellingsen , Ying Mei , * Center for Astrophysics, GuangZhou University, Guangzhou 510006, China; [email protected] School of Physical Sciences, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
Received 2018 February 6; accepted 2018 October 16
Abstract
That the laws of physics are the same at all times and places throughout the Universeis one of the basic assumptions of physics. Astronomical observations provide the only meansto test this basic assumption on cosmological time and distance scales. The possibility ofvariations in the dimensionless physical constant µ - the proton-to-electron mass ratio, can betested by comparing astronomical measurements of the rest frequency of certain spectral linesat radio wavelengths with laboratory determinations. Different types of molecular transitionshave different dependencies on µ and so observations of two or more spectral lines towardsthe same astronomical source can be used to test whether there is any evidence for eithertemporal or spatial changes in the physical fundamental constants. µ will change if the relativestrength the strong nuclear force compared to the electromagnetic force varies. Theoreticalstudies have shown that the rotational transitions of some molecules which have transitionsin the frequency range which will be covered by the FAST (e.g., CH OH, OH and CH) aresensitive to changes in µ . A number of studies looking for possible variations in µ have beenundertaken with existing telescopes, however, the greater sensitivity of FAST means it willopen new opportunities to significantly improve upon measurements made to date. In thispaper, we discuss which molecular transitions, and sources (both in the Galaxy and externalgalaxies) are likely targets for providing improved constraints on µ with FAST. Key words:
ISM: molecules — Radio lines: ISM — Techniques: radial velocities — ele-mentary particles
Theories beyond the standard model of physics have predicted the possibility of space-time variation in thefundamental constants. Over the last few decades a number of laboratory studies, theoretical calculationsand astronomical observations have been conducted to search for the signatures of such variations (for a
X. Chen, S. P. Ellingsen & Y. Mei recent review of the field see Uzan (2011). Astrophysical spectroscopic studies have mostly focussed onsearching for variations in the fine structure constant α = e/ ~ c , and the proton-to-electron mass ratio µ = m p /m e . Astrophysical spectroscopy can be used to search for changes in the dimensionless constants α and/or µ by comparing the rest frequency of different transitions in atoms and molecules as a function oftime and/or position. The energy levels of different quantum states can be expressed in terms which includethe dimensionless constants α and µ . Where a transition takes place between energy levels with differentdependencies on these constants a variation in either will cause a change of the transition frequenciescompared to the laboratory value (e.g., Reinhold et al. (2006); Webb et al. (1999)). The change in frequencycaused by a change in either of these dimensionless constants is characterized by the sensitivity coefficientof transition K α or K µ (which is defined as the proportionality constant between the fractional frequencyshift of the transition, ∆ ν/ν and the fractional shift in α or µ ) as follows: ∆ νν = K α ∆ α α + K µ ∆ µ µ . (1)The rest frequency of electron transitions in atoms is generally more sensitive to the fine structureconstant α , whereas rotational transitions in molecules have a stronger dependence on the proton-to-electronmass ratio µ . The mass of the proton is set by the strong nuclear force, while the mass of the electron is set byweak-electromagnetic force, any change in the relative strength of these two fundamental interactions willchange µ and hence the rest frequency of rotational transitions. One mechanism which may cause variabilityof the two constants is through the scalar fields which are potential candidates for producing dark energy,which is responsible for the observed cosmic acceleration. The chameleon mechanism proposes that thescalar fields are ultra-light in the cosmic vacuum but effectively possess a large mass locally when theyare coupled to ordinary matter (Khoury & Weltman 2004). Therefore the searches for changes in µ and α are especially important for not only understanding the nature of the fundamental laws of physics, but alsoproviding direct observational tests for some cosmological theories.Furthermore models of dynamical scalar fields predict relationships between variations in different di-mensionless constants such as µ and α with time, for example: ˙ µµ = R ˙ αα , (2)where R is a scalar argued to be of order -40 to -50 (Avelino et al. 2006; Thompson 2013; Thompson etal. 2013). Values of R of this order imply that variations in µ will be easier to detect than those in α . Thismeans that upper limits on variations in µ at relatively low redshift can significantly constrain variations in α at higher redshift for example if rolling scalar fields are the mechanism through which they are produced.The most sensitive searches for possible spatial or temporal variations of µ require high signal to noiseobservations of the molecular transitions that have a large sensitivity coefficient K µ . Previous searchesfor variations in µ on cosmological timescales have compared optical transitions of molecular H (themost abundant astrophysical molecule), in high-redshifted objects with accurate laboratory measurements(Reinhold et al. 2006). These observations show that ∆ µ/µ < × − over look-back times of ∼
12 Gyr.However, the H transitions measured in these observations have relatively poor K µ sensitivity coefficientsin the range -0.05 < K µ < +0.02. Rotational transitions of molecules are generally much more sensitive tochanges in µ ( K µ ∼ ) than rovibrational transitions of H , therefore more recent observational studies onstraints on µ with FAST 3 have focused on searching for changes in µ using rotational transitions of molecules at radio wavelengths.Some molecular transitions have even greater sensitivity to changes in µ than the majority, for example, theinversion transitions of ammonia (NH ) have K µ =-4.46. Hence the ammonia inversion transitions are ∼ µ than the H transitions in the optical wavelength range. Astronomicalobservations of NH transitions at radio wavelengths have been used to constrain ∆ µ/µ < . × − (1 σ )in the z = 0 . lensing galaxy in the PKS1830-211 gravitational lens system (Henkel et al. 2009) and ∆ µ/µ < . × − in the z = 0 . absorbing galaxy towards the radio source B0218+357 (Kanekar etal. 2011). In the nearby universe observations of NH transitions towards molecular clouds in the MilkyWay have been used to constrain variations in µ to be ∆ µ/µ < × − ( σ ; Levshakov et al. (2013)).However these limits are achieved by comparing the spectral profile of NH inversion transitions with lesssensitive ( K µ ∼ ) transitions from different species, such as cyanopolynes in particular HC N transitions.This approach suffers from difficult to quantify systematic effects due to the unknown degree of chemi-cal segregation between the different molecular species (i.e. due to different and inhomogeneous spatialdistributions of the different molecules along the line of sight).The major limitation on observations of molecular transitions at radio and millimetre wavelengths is thatmost common astrophysical molecules have the same, or very similar dependency on µ , for all of their tran-sitions. A recent breakthrough has been the discovery that the hindered internal rotation which producesthe rich microwave spectra observed in some polyatomic molecules (e.g. methanol CH OH, and methylmercaptan CH SH) also causes a significant enhancement in K µ compared to those observed in rotationaltransitions in any other molecule commonly found in interstellar space, including NH (Jansen et al. 2011a,2013; Levshakov et al. 2011). Furthermore, the different transitions of these molecules have different K µ coefficients, meaning that they offer the opportunity to tightly constrain µ using observations of a singlemolecular species, thus avoiding chemical segregation issues that arise when comparing transitions associ-ated with different molecules. The high K µ transitions are generally those between near degenerate levelsof these molecules, hence they are typically at low radio frequencies. The low radio frequency range willbe well covered by the Five-Hundred-Meter Aperture Radio Telescope (FAST). FAST will open new pos-sibilities for making sensitive observations of weak molecular emission from high- z astronomical objects.In this paper, we discuss the molecular transitions and sources (both in the Galaxy and external galaxies)which are likely to provide the best opportunity to make sensitive searches for possible variations in µ withFAST. FAST is a current Chinese mega-science project to build the largest single dish radio telescope in the world.The telescope consists of a 500-meter aperture with an illuminated aperture of 300-meters. The telescopeis located in the Guizhou province, China, and the first phase covers a continuous frequency range, 70MHz – 3 GHz using a set of 9 receivers (see Nan et al. (2011); Li et al. (2018)). The L-band 19-beamreceiver is the main instrument for surveys of H I and pulsars in the Galaxy and nearby galaxies. The designspecifies the system temperature and resolution at L band to be ∼
25 K and 3 ′ , respectively. The declinationrange of FAST is -15 ◦ – 65 ◦ . The combination of large collecting area and advanced receiver and backend X. Chen, S. P. Ellingsen & Y. Mei systems means that FAST will be an important instrument for advancing our understanding of cosmology,galaxy evolution, the interstellar medium life cycle, star formation and exoplanets. A spectroscopic surveyof Galactic and extragalactic objects with continuous coverage between 70 MHz – 3 GHz is one of themain scientific programs which has been started with FAST (Li et al. 2013, 2018). This frequency rangeincludes a number of important molecular transitions with different sensitivity to variations in µ and theseare discussed in Section 3. Table 1 summarizes the molecular transitions which are sensitive to variations in the proton-to-electron ratioand have rest frequencies in the 70 MHz – 3 GHz range which will be covered by FAST. OH and its isotopes
Methanol (CH OH) is one of the simplest molecules that exhibits hindered internal rotation and thus hasbeen the subject of a number of theoretical and observational studies relating to variations in the proton toelectron mass ratio (e.g.,Ellingsen et al. (2012); Jansen et al. (2011a,b); Levshakov et al. (2011)). Methanolis a widespread interstellar molecule observed in numerous regions in the Galaxy and in some externalgalaxies (e.g., Herbst & Van Dishoeck (2009); Mart´ın et al. (2006); Sjouwerman et al. (2010)). In thelocal universe methanol emission is commonly observed in the vicinity of high-mass star forming regionsexhibiting both maser and thermal emission from hot cores. Absorption is also detected toward cold cloudsin the foreground of continuum sources. There are more than 30 methanol transitions known to exhibit maseremission with wavelength in the range from centimeter to millimeter. These transitions are empiricallyclassified into two types which are known as class I or class II transitions on the basis of the locationswhere they are observed to arise in the star forming region – class I methanol masers usually arise frommultiple positions within a star forming region and are distribued on scales of 0.1–1.0 parsec, whereas classII methanol masers are found within ∼ ′′ of high-mass young stellar objects (e.g., Batrla & Menten (1988);Plambeck & Menten (1990)). Over one thousand methanol maser sources have been detected in our Galaxy,including ∼
900 class II (e.g. Green et al. (2009)) and ∼
400 class I methanol maser sources (see the reviewof ( ? )). Observations of both class I and class II methanol masers within the Milky Way have recently beenapplied to constrain spatial variations in µ at the level of ∆ µ/µ < × − ( σ ; (Ellingsen et al. 2011)Levshakov et al. 2011). However, at cosmologically interesting distances there is only one detection ofmethanol and that is in absorption towards PKS B1830-211. This system is a gravitationally lensed quasarand the absorption occurs in the lensing galaxy which is at a redshift of z = 0 . . Observations of threedifferent methanol transitions with rest frequencies of 12.2, 48.3 and 60.5 GHz have been used to constrainvariations in µ on temporal scales of around 7 Gyr (the look-back time to z = 0.89) (Bagdonaite et al.2013a,b; Muller et al. 2011) Ellingsen et al. 2012; The most sensitive of these observations by Bagdonaiteet al. constrain ∆ µ/µ to be less than × − (2 σ ). An important point to note for FAST searches is thatthe rest frequencies of the methanol transitions detected in the PKS B1830-211 system far exceed the upperfrequency limit of the first phase of FAST (3 GHz). The class II and class I methanol masers with the lowestrest frequencies are the − A + transition at 6.7 GHz and the − − − E transition at 9.9 GHz, onstraints on µ with FAST 5 respectively. These two transitions are also very sensitive to variations in µ with K µ =-42 and 12, for the6.7 and 9.9 GHz transitions, respectively. These transitions cannot be used to look for variations in µ in theMilky Way or nearby galaxies with FAST, however, where they may be present in galaxies at redshifts of > , they would be within the detectable frequency range.Theoretical calculations show that some lower-frequency methanol transitions which have not been thetarget of previous searches for variations in µ possess larger sensitivity coefficients than the most commonlyobserved methanol maser transitions (Jansen et al. 2011a,b). We have collated a list of those transitions ofmethanol and its isotopologues which lie within the FAST frequency range and list them in Table 1. We alsolist the information for the lowest rest frequency transitions for both class I and class II methanol masers inthis table, since they are potential candidates for measuring temporal variations in µ through observationsof high- z objects with FAST, we discuss this further in Section 4. The equivalent transitions of methanolisotopologues are generally more sensitive to changes in µ than those of methanol itself. The most sensitiveof the methanol isotopologues with K µ =
330 is the − E transition of CD OH which has a restfrequency of approximately 1.2 GHz. The sensitivity of this transition to variations in µ is approximatelyone order of magnitude larger than that of the highest K µ methanol transitions used in previous studies. Thisdemonstrates that the detection of methanol isotopologues would significantly help to make more sensitiveinvestigations for variations in µ . Emission from methanol isotopologues has been detected in both high-mass and low-mass star forming regions in the Milky Way, for example CH OH and CD OH have beendetected by Parise et al. (2002, 2004) and Ratajczak et al. (2011), showing that these isotopologues arepresent at detectable abundances in the local universe. Although it should be noted that the detections of themethanol isotopologues were from transitions at millimeter wavelengths rather than the lower frequencytransitions suitable for observations with FAST.It is worth noting that the sensitivity coefficients of the transitions of methanol and its isotopologueslisted in Table 1 have both large positive and large negative values. This means that a variation in µ will shiftthe frequency of some transitions to higher frequencies while others shift to lower frequencies. So the mostsensitive method for accurately probing for variations in µ is through simultaneous observations of differenttransitions with large positive and negative values of K µ . Observations of different isotopologues also havethe advantage that they avoid many systematic effects that can affect comparisons based on transitions ofdifferent molecules (such as chemical segregation). In addition to methanol, the frequency range of FAST will also cover transitions of other important inter-stellar molecules which have good sensitivity to variations in µ . These other molecules and the relevanttransitions are also listed in Table 1. CH is abundant in the Universe and the two ground-state Λ -doublet transitions for Π / J = 3 / and J = 1 / which have rest frequencies of ∼ . and ∼ . GHz, respectively, have been observedtowards numerous clouds in the Milky Way (e.g., (Genzel et al. 1979; Whiteoak et al. 1978; Ziurys etal. 1985). The 3.3 GHz transition has also been detected in other galaxies (e.g., Whiteoak et al. (1980)).Theoretical calculations show that the two Λ -doublet transitions of CH are very sensitive to changes in X. Chen, S. P. Ellingsen & Y. Mei µ with K µ ranging from 1.7 – 6.3 (Kozlov 2009). Simultaneous astronomical observations of the two Λ -doublet transitions of CH have been undertaken to constrain µ -variations at σ upper bounds of ∆ µ/µ < × − in our Galaxy (Truppe et al. 2013). It should be noted that the frequency of J = 1 / transitionsare slightly above the 3 GHz upper limit of the first stage receivers being developed for FAST. This means itwill not be possible to constrain variations in µ for Galactic objects with the two Λ -doublet transitions of CHsimultaneously with FAST. However FAST will be suitable for simultaneously measuring both transitionsfor moderate redshift objects (e.g. z > . ). The higher sensitivity of FAST will open the opportunity todetect relatively weak emission from this molecule in high − z objects. OH is a very common interstellar molecule and has been widely observed in our Galaxy and externalgalaxies. Maser emission from the OH molecule has been observed from a number of transitions, for exam-ple the ground-state transitions ( Π / , J = 3 / state), and many excited state-state transitions (including Π / , J = 1 / at 4765 MHz, and Π / , J = 5 / at 6035 MHz). Of the various OH maser transitions the1665/1667 MHz ground-state transitions in star forming regions are usually the strongest. At present about ∼ OH maser sources have been detected in our Galaxy, most of them are stellar masers associated withevolved stars (see Mu et al. (2010)). At present only ∼
400 OH masers have been detected in star formingregions (see Qiao et al. (2014)), however, current sensitive OH maser surveys such as SPLASH (Dawsonet al. 2014) and future surveys such as GASKAP (Dickey et al. 2013) will significantly increase the num-ber of OH maser sources in the Galaxy (both evolved star and star forming regions). In external galaxies,over one hundred galaxies with OH megamaser activity have been found (e.g, (Baan et al. 1998; Darling &Giovanelli 2002)). Similar to CH, the Λ -doublet transitions of OH potentially also provide a very sensitiveindicator for searching for variations in µ (Kozlov 2009). Observations of the ground-state 18cm OH linesin absorption at z = 0 . , have been used to constrain the variation in µ to be ∆ µ/µ < . × − fora look-back time of 6.7 Gyr (Kanekar et al. 2012). However, in that work the 21 cm hydrogen line wasadopted as a reference. Detection of more than one Λ -doublet transition of OH offers the opportunity tofurther improve the constraint. Within the frequency coverage of the first stage of FAST, there are two OH Λ -doublet transitions at Π / J = 3 / and Π / J = 9 / which may enable such observations to beundertaken. The Π / J = 9 / transitions are very sensitive to changes in µ with the sensitivity coefficient K µ ranging from 210 – 460, which is more than two orders of magnitude greater than that of the 18 cm OHlines used in previous studies. To date, the higher J − transitions of OH in the 88 – 192 MHz range have notbeen observed in interstellar space. If these transitions can be detected in either Galactic or extragalacticobjects with FAST, it opens up the possibility to make very sensitive studies for variations in µ using si-multaneous observations of these OH transitions in combination with ground-state OH. However, we notethat these higher − J transitions are at significantly higher energies ( E upper = 875 K) than the 18-cm lines,hence they may have a different spatial distribution to the ground-state transitions. This issue can be onlyclarified through detection and observation of these transitions. CH NH is a relatively small and stable molecule which is abundant in the Milky Way (e.g., Lovaset al. (2004)). It has also been detected in a spiral galaxy at redshift z = 0 . (the lensing galaxy inthe 1830-211 system ; Muller et al. (2011)). CH NH has hindered internal rotation of the CH groupwith respect to the amino group (NH ) which is similar to what occurs in methanol. In addition to this onstraints on µ with FAST 7 it also has tunneling associated with wagging of the amino group. Ilyushin et al. (2012) have used thismolecule to search for temporal variations in µ through observations at millimeter wavelengths towards the z = 0 . intervening galaxy in the PKS 1830-211system. However, the relatively low sensitivity K µ for thetransitions observed means that it was not possible to place tight constraints on variations in µ from thoseobservations ( ∆ µ/µ < × − ). Within the frequency coverage of FAST, there are multiple CH NH transitions, one of which is very sensitive to variations in µ (Ilyushin et al. 2012). The sensitivity of thevarious transitions have K µ spanning the range -1 – -19 and observations in these transitions offer thepotential to make sensitive searches for variations in µ with FAST. CH SH is the sulphur analogue of methanol, therefore similar to methanol it experiences hindered in-ternal rotation which results in larger sensitivity to variations in µ . There are multiple transitions of CH SHwhich lie within the frequency coverage of FAST, and these have a large spread in their K µ sensitivitycoefficients which span an approximate range of -15 –12 (Jansen et al. 2013). It should be noted that thefrequency of the − A + transition, which has the greatest sensitivity to variations in µ ( K µ = − . is above the 3 GHz upper limit of the FAST frequency coverage, however, this transition will be a candidatefor observations in objects with moderate redshifts. To date, CH SH has only been detected in the MilkyWay (e.g., Gibb et al. (2000); Linke et al. (1979)), however, the high sensitivity of FAST will likely make itpossible to detect this molecule in some external galaxies. C H O has recently been shown to have low-frequency transitions (within the FAST frequency cov-erage) which are sensitive to variations in µ , with K µ ranging from -17 (for the 882.2 MHz transition)to 18 (for the 978.3 MHz transition). Viatkina et al. (2014) have calculated the K µ sensitivity coefficientfor approximately 10 transitions which lie within the FAST frequency range (see Table 3 of Viatkina etal. (2014)). Here we list only those transitions with larger K µ values in Table 1. This molecule has beendetected in interstellar space in the comet C/1995 O1 (Hale-Bopp; (Crovisier et al. 2004)) and in molecularclouds in the center of the Milky Way (Hollis et al. 2002), although the transitions observed to date are fromhigher frequency transitions beyond the upper limit of the FAST frequency coverage. It is very likely thatthe high sensitivity of FAST will enable the detection of the lower frequency transitions of interest here,both in the Milky Way and perhaps also in some extragalactic sources. In this section, we discuss which sources in our Galaxy and other galaxies are prime targets for FASTobservations to search for possible spatial and temporal variations in µ . We mainly focus on targets for themethanol and OH transitions because they possess the largest sensitivity coefficients to variations in µ (oneto two orders of magnitude more sensitive than most molecular transitions) and are widespread throughoutthe Galaxy and external galaxies, compared to some of the other less abundant molecules discussed inSection 3. Sources which exhibit maser emission (including OH, CH OH and H O) may provide the best target sam-ples for searches for possible variations in µ in the Milky Way. The strongest maser emission is usually X. Chen, S. P. Ellingsen & Y. Mei observed from the molecular gas associated with massive star forming regions. These clouds consist of gaswhich contains relatively high abundances of both simple and complex molecular species, including themolecules which have the greatest sensitivity to variations in µ such as OH and methanol.Observations focusing on transitions of the methanol isotopologues (such as CH OD, as discussed inSection 3.1) can potentially provide the most sensitive tests for variations in µ . For a source to exhibitmethanol maser emission it must have a relatively high abundance of the methanol molecule, therefore suchregions are likely to provide the best targets for detections of the methanol isotopologues. There are overone thousand methanol maser sources (including class I and class II transitions) which have been detectedin our Galaxy. In addition to these known methanol maser detections from the past surveys, e.g. Parkesmethanol multi-beam survey at 6.7 GHz class II transition (Green et al. 2009), a number of new methanolmaser surveys in our Galaxy are underway or proposed. In particular, a series of targeted surveys for classI methanol masers at 95 GHz transition have detected about 200 new class I methanol maser sources, andcombined with previous observations they have increased the number of known class I methanol masersin our Galaxy to ∼
400 (Chen et al. 2011, 2012; Chen et al. 2013; Gan et al. 2013). Statistical analysisof these surveys has been used to predict that our Galaxy may contain at least ∼ µ variation observations in both OH and methanol transitions in the northern hemisphere. The prime extragalactic targets to search for variations in µ are those which host OH megamaser emission,as observations of multiple OH transitions can provide strong constraints. OH megamaser emission has beendetected in over 100 galaxies in surveys undertaken to date (e.g, Baan et al. (1998); Darling & Giovanelli(2002)), however, most of the detected OH megamaser galaxies are at relatively low redshifts with z < . . onstraints on µ with FAST 9 A survey for OH megamasers in high- z galaxies is required to place the most stringent constraints on vari-ations in µ over the history of the Universe. OH megamaser searches in high- z galaxies are also one of themain early science projects for FAST (see Zhang et al. (2012) and Li et al. (2013)). Moreover, simultane-ous H I observations towards OH megamaser galaxies with FAST also provide opportunities to constrainvariations in µ , although the systemic effects due to comparing observations from different molecules aredifficult to quantify and remove, as it is never really possible to determine the extent to which they arisefrom different locations and to which the observed spectral differences are due to different line of sightmotions from the two transitions.There are approximately 10 extragalactic detections of CH emission (Bottinelli et al. 1991; Whiteoak etal. 1980) and these represent potential targets for searching for variations in µ . They are however, all rela-tively nearby galaxies and therefore it will not be possible to simultaneously observe the two CH transitionslisted in Table 1 with FAST. The galaxies towards which CH emission has been detected often also exhibitstrong OH absorption and some sometimes H O emission. Therefore moderate redshift galaxies ( z > O emission are potential targets for future CH observations with FAST.In particular, H O megamaser galaxies may be good targets because they can be detected at relatively highredshifts, with the most distant source being at z = 2 . (MG J0414+0534; Impellizzeri et al. (2008b)).Targets suitable for using methanol transitions to investigate possible changes in µ are at present limitedto one extragalactic source outside the nearby galaxies. The lensing galaxy in the PKS B1830-211 grav-itational lense system is at a modest redshift of z = 0 . and absorption from three different methanoltransitions has been detected towards it (Bagdonaite et al. 2013a,b; Ellingsen et al. 2012; Muller et al.2011). Emission from a number of thermal methanol transitions at millimeter wavelengths (mainly the k − k E series at 96.7 GHz) has been detected towards a handful of nearby galaxies (e.g.,(Henkel et al.1987; H¨uttemeister et al. 1997)). However the detected emission from these thermal lines is weak and broad,and hence is unlikely to be able to provide useful constraints or tests for variations in µ (see (Ellingsen et al.2011)). While the absorption of methanol may provide a more efficient approach for such constraints sinceits spectrum is usually narrow, moreover besides the PKS B1830-211 discussed above, methanol absorp-tion is also detected in the nearby galaxy NGC3079 (Impellizzeri et al. 2008a), suggesting that methanolabsorption may be common in external galaxies. More sensitive searches for methanol emission (prefer-ably maser emission) or absorption in nearby extragalactic sources is required to better understand how theproperties of these sources are influenced by their environment (factors such as metallicity and uv flux). Anumber of searches have been made for class II methanol megamasers at 6.7 and 12.2 GHz transitions to-wards samples selected from OH and H O megamaser galaxies, and/or (Ultra-) Luminous Infrared Galaxies([U]LIRGs) (Darling et al. 2003; 1Ellingsen et al. 1994; Norris et al. 1987; Phillips et al. 1998). To datemore than one hundred sources have been searched, without any detections. It may be, as suggested byPhillips et al. (1998), that the mechanisms which produce high methanol abundance in individual star for-mation regions may not operate with sufficient efficiency on the larger scales needed to produce class IImegamasers. Alternatively, it may be that the sensitivity of previous searches was not high enough to detectmaser emission in these sources or that appropriate targeting criteria have not been identified to search forclass II methanol megamasers. A sensitive survey for class II methanol megamasers towards a large sample of sources with FAST would clarify these issues. Although for the first stage of FAST the targets for 6.7GHz class II methanol megamaser searches must be at redshifts of z > . , in order for the emission to bedetectable in the frequency range of the telescope.In contrast to class II methanol transitions, theoretical models suggest that it is perhaps more likelythat class I methanol transitions can be excited on large scales in the central regions of luminous galaxies(Sobolev 1993). The recent detection of widespread methanol maser emission in the 36 GHz class I tran-sition toward the center of the Milky Way (Yusef-Zadeh et al. 2013), further supports the theory. Based onthese results, the first sensitive survey for class I methanol megamasers in the 36 GHz transition was under-taken towards a sample of OH megamaser galaxies with the Australia Telescope Compact Array, and hasproduced the first extragalactic detections of this transition towards NGC 253 (Chen et al. 2018; Ellingsenet al. 2014, 2017), Arp 220 (Chen et al. 2015), NGC 4945 (McCarthy et al. 2017), IC 342 and NGC 6946(Gorski et al. 2018). Further comparison with the infrared, radio and molecular emission, and star formationrates of the host galaxies with/without detections will enable us to refine targeting criteria for future obser-vations. Then by compiling a reliable target sample based on these criteria, the 9.9 GHz class I methanoltransition can be searched towards galaxies meeting these criteria at redshifts z > . with FAST. The de-tection of two or more methanol megamaser transitions in high- z galaxies offers the best current prospectsfor making sensitive observations for variations in µ at larger look-back times. Thanks to the large collecting area and advanced receiver and backend systems, FAST should becomeone of the most important instruments for searching for possible variations in the proton-to-electron massratio µ on cosmological time and distance scales. Within the frequency coverage of FAST, there are anumber of transitions of abundant interstellar molecules (e.g., CH OH, OH and CH) which are − orders of magnitude more sensitive to variations in µ than those typically used in current studies. Existingand ongoing surveys for methanol and OH masers in our Galaxy appear to provide the best samples forobservations to determine if µ varies spatially in the local universe. However, further surveys for OH, CHand methanol megamasers in high- z galaxies are required to provide good quality targets for investigationsof variations in µ on cosmological time scales. It is our hope that the potential importance of these molecularmegamasers for testing variations in µ will stimulate broader surveys for these sources with FAST. FASTobservations utilising the most sensitive molecular transitions are likely to improve the evidence either foror against the presence of variations in the proton-to-electron mass ratio by more than − orders ofmagnitude beyond the best current limits. Acknowledgements
This work was supported by the National Natural Science Foundation of China(11590781), the Strategic Priority Research Program of the Chinese Academy of Sciences (CAS; GrantNo. XDA04060701), Key Laboratory for Radio Astronomy, CAS.
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Table 1
Selected molecular transitions and K µ coefficients for the FAST search Molecules Transitions Rest Frequency (MHz) K µ Ref. CH OH − A ∓ − A + a − − − E a CD OH − E − E − E − A + CH OH − A − CD OD − − E − − − E CH OH − − − E Π / J = 3 / F = 2 − F = 1 − F = 2 − F = 1 − Π / J = 1 / F = 0 − a F = 1 − a F = 1 − a Π / J = 3 / F = 1 − F = 1 − F = 2 − F = 2 − Π / J = 9 / F = 5 − F = 5 − F = 4 − F = 4 − NH A − A B − B A − A A − A B − B SH − A ∓ − A ∓ − E − A + a H O , v = 0 − , v = 1 , v = 0 − , v = 1 , v = 0 − , v = 1 , v = 1 − , v = 0 , v = 0 − , v = 1 Notes: The frequency of these transitions is beyond the upper limit of 3 GHz of FAST frequency coverage.These transitions can be only used to constraint on µµ