Molecular astronomy of cool stars and sub-stellar objects
aa r X i v : . [ a s t r o - ph . S R ] D ec October 22, 2018 2:37 Dynamical Systems AstroReview-test
Dynamical Systems
Vol. 00, No. 00, Month 200x, 1–33
RESEARCH ARTICLEMolecular astronomy of cool stars and sub-stellar objects
PETER F. BERNATH ∗ Department of Chemistry, University of York, Heslington, York, YO10 5DD UK ( v3.5 released January 2009 )The optical and infrared spectra of a wide variety of ‘cool’ astronomical ob-jects including the Sun, sunspots, K-, M- and S-type stars, carbon stars, browndwarfs and extrasolar planets are reviewed. The review provides the necessaryastronomical background for chemical physicists to understand and appreci-ate the unique molecular environments found in astronomy. The calculation ofmolecular opacities needed to simulate the observed spectral energy distribu-tions is discussed. Keywords: extrasolar planets, cool stars, brown dwarfs, solar spectra,sunspots, spectral energy distributions, molecular opacities, astronomicalspectroscopy ∗ Email: [email protected]: 1468-9375 print/ISSN 1468-9375 onlinec (cid:13) ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath
Contents
1. Introduction2. Astronomy Background3. The Sun and Sunspots4. K and M Stars5. Brown Dwarfs6. AGB, S and C Stars7. Extrasolar Planets8. Molecular Opacities9. Conclusions10. References
1. Introduction
Molecules are associated with the ‘cold’ Universe. Historically astronomers first studiedthe spectra of hot, bright stars full of atomic emission and absorption lines. Except for thenearby Sun, cooler stars with molecular lines are fainter and more difficult to observe. Asthe surface temperature drops, the star reddens and the peak of the emission curve shiftsto the infrared. (The Wien displacement law for a blackbody, λT = 2898 µ m K, gives amaximum at 1 µ m for 2898 K. [1]) The total radiated power also varies approximately asthe fourth power of temperature (from the Stefan–Boltzmann law [1]), in so far as stellaremission is approximated by a blackbody. The spectroscopic study of ‘cool’ sources withsurface temperatures in the range of about 500 − ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects T ), pressure and Gibbs free energy of formation(∆ G f ( T )) of all possible compounds as a function of temperature [8]. In this case, thecoupled algebraic equations that describe the equilibria need to be solved simultaneouslyto determine the composition, as is customary in chemical thermodynamics.
2. Astronomy Background
Big Bang nucleosynthesis created only the elements H, He and a trace of Li some 13.7billion years ago [9, 10]; all other elements are formed in stars [11, 12]. After the BigBang, the early Universe expanded rapidly and cooled. After a few hundred million years,gravitational attraction produced the first stars, the ‘Population III’ class of objects[13]. Little is known about this first generation of stars because they have not beendetected yet with certainty; a few molecules such as LiH are predicted to form in theearly Universe [14]. Models predict that population III stars were massive (more than onehundred solar masses) and their intense UV emission ionised the surrounding interstellarmedium. Massive stars burn the H and He fuel rapidly to form the elements up to Fe inthe periodic table by nuclear fusion reactions. The Fe nucleus is the most stable in termsof binding energy per nucleon so fusion reactions are unable to make any heavier elements.After a few million years of life Population III stars began to collapse as the nuclear fuelwas exhausted, and they exploded as supernovae. Nuclear reactions during supernovaexplosions release a rapid burst of neutrons ( r -process) that are absorbed by nuclei and ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath make elements heavier than iron. Some heavy elements are also produced by nuclearreactions in stellar cores from the slow neutrons ( s -process) released in fusion reactions.Supernova explosions and stellar winds therefore return matter to the interstellar mediumenriched in ‘metals’. In astronomy all elements other than H and He are termed metals.The Population II class of stars were created by the gravitational collapse of matter inthe interstellar clouds that formed from the metal-enriched ejecta of Population III stars.Population II stars are still depleted in metals compared to younger stars like our Sunthat are part of Population I. The elemental abundance of a star is a crucial property andour own Sun is taken as a standard reference. Astronomers have defined the metallicityof a star as the abundance ratio of iron to hydrogen as compared to the same ratio inthe Sun, i.e. the metallicity [Fe/H] is defined as[Fe / H] = log (cid:18) ( N Fe /N H ) star ( N Fe /N H ) Sun (cid:19) = log (cid:18) N Fe N H (cid:19) star − log (cid:18) N Fe N H (cid:19) Sun (1)so a metallicity of 0 corresponds to the same relative Fe abundance as the Sun. Fe is cho-sen for measurement convenience, and metallicities of − − − −
6, i.e. Fe depleted by more than a factorof a million, are expected. A few low mass stars with metallicites as small as − . −
9) so at 5800 K our Sun is a G2 dwarf. ‘Early’ M’s(or other stellar types) refer to low numbers and ‘late’ M’s to cooler higher numbers.The classification of stars is two dimensional, based both on surface temperature (e.g.G2 for 5800 K) and ‘size’ (luminosity). In practice there are three main categories forluminosity: supergiant (I), giant (III) and dwarf (V), although five Roman numerals (I toV) are used. Luminosity (with 1 L ⊙ = 3 . × W equal to the luminosity of the Sun)is used for convenience instead of the more difficult to determine mass (in units of solarmasses, 1 M ⊙ = 1 . × kg). Dwarfs are the largest category and our Sun is thusclassified as a G2 V star. Stellar interiors have temperatures of millions of degrees (e.g. 15million K for our Sun), but they are not visible from the exterior because of the ‘opacity’of stellar atmospheres. Implicit in the stellar main sequence is the correlation betweenmass and surface temperature: massive stars burn their nuclear fuel more rapidly andhave higher surface temperatures.In practice stellar classification is based on the presence or absence of key atomic andmolecular features in the spectrum [17], which is sometimes called the spectral energydistribution. A-type stars have strong hydrogen lines and the coolest stars have strongnear infrared bands of electronic transitions of diatomic TiO and VO. Recently, objects ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects − − − −
2. In fact the lack of metals in cool subdwarfs means that the opacityof the stellar atmosphere is decreased so that subdwarfs can be more luminous in thevisible than dwarfs (i.e. subdwarfs are not necessarily ‘sub-luminous’). The terms dwarf,brown dwarf and subdwarf therefore refer to different kinds of objects.Not all stars lie on the ‘main sequence’ discussed above. Clearly very young stars—young stellar objects or YSOs—that have just been born in dark interstellar clouds donot lie on the main sequence. YSOs will evolve until they are main sequence stars andthen spend most of their life on the main sequence [5]. Similarly when low-mass starssimilar to our Sun convert most of their H nuclear fuel into He, they evolve off the mainsequence and become red giants [21, 22]. Red giants burn He in their cores to make C,and their outer shells expand and cool. The red giant phase is followed by a complexAGB (asymptotic giant branch) phase where the core consists of mainly C and O withenergy coming from the fusion of He and/or H in thin surrounding shells [21]. During theAGB phase strong stellar winds return much of the matter to the interstellar mediumand the object evolves towards a planetary nebula. AGB stars often possess circumstellarshells of dust and molecules which envelop the star and render it nearly invisible in theoptical region. In a planetary nebula the circumstellar shell has become detached fromthe hot central stellar core. A planetary nebula is a spectacular short-lived phase (afew thousand years) in which the surrounding cloud of matter glows in the visible fromthe intense UV excitation of the very hot central star. Ultimately the cloud of matterdissipates and the central star becomes a white dwarf.High-mass stars with stellar masses greater than about 8 M ⊙ will explode as Type IIsupernovae, unless mass-loss is sufficiently rapid [23]. In essence, high-mass stars consumetheir nuclear fuel until a sufficiently large ( > . M ⊙ , the Chandrasekhar limit) inertFe/Ni core remains in which nuclear fusion is no longer possible. The heat production ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath of the core is insufficient to support the outer layers and gravitational collapse ensues,rapidly releasing an enormous quantity of energy. The outer layers of the star disintegrateand ultimately the core ends up as a neutron star or a black hole.The ratio of carbon to oxygen abundance, C/O, is a crucial parameter. Normal starson the main sequence have C/O less than 1 and when molecules begin to form CO isalways present because of its strong triple bond. The formation of CO ties up most of thecarbon and an oxygen-rich chemistry results. If C/O is greater than 1 then the formationof CO ties up all of the oxygen and a very different carbon-rich chemistry is possible. Redgiant and AGB stars produce carbon from helium so the composition of stars that are nolonger on the main sequence becomes increasingly carbon rich. When the abundance ofcarbon and oxygen are equal then S-type stars (see below) result [24] and when carbonis more abundant than oxygen then carbon stars (C-type stars) form [25]. Carbon starsare therefore red giant or AGB stars with C/O > M J = 0 . × − M ⊙ = 318 M ⊕ ), which has asurface temperature less than 200 K, are believed to fall on the same main sequence asbrown dwarfs. Hundreds of extrasolar planets have been discovered primarily by the verysmall periodic Doppler shifts they induce in the absorption lines of the spectrum of theparent star [26, 27]. A few extrasolar planets have been detected by the small decreasein luminosity observed when they transit in front of the star. There is a selection effectthat preferentially favours the discovery of ‘hot Jupiters’ because massive planets withshort periods are easier to find. Extrasolar planets are therefore closely related to browndwarfs and will be included in the set of cool objects covered in this review.
3. The Sun and Sunspots
As our nearest and most important star, the Sun holds a special position in astronomyand its study is part of a separate sub-discipline. The Sun has an effective surface tem-perature of 5800 K, which dissociates all polyatomic molecules. Lines of neutral atomsand atomic ions dominate the solar spectrum as first observed by Fraunhofer in thevisible region. Fraunhofer had no explanation for the dark absorption lines in the solarspectrum and labelled them with letters starting with A in the near infrared at 760 nm.Apart from the A- and B-lines (which are the forbidden A- and B-bands of terrestrialO , i.e. the 0-0 and 1-0 vibrational bands of the b Σ +g − X Σ − g electronic transition), allof the Fraunhofer lines are due to atoms; for example, the C-line at 656 nm is the firstH Balmer line (H α ) and the D-line contains the two Na D-lines (589.0 and 589.6 nm).A handful of diatomic molecules contribute weakly to the near infrared, visible andnear UV solar spectra [26, 29]: MgH A Π − X Σ + [30, 31], C Swan bands (d Π g − a Π u )[32], CH B Σ − − X Π and A ∆ − X Π [33], CN B Σ + − X Σ + (Violet System) [34] andA Π − X Σ + (Red System) [35]. Solar spectra in this region have been recorded with the1-m Fourier transform spectrometer (FTS) at the McMath–Pierce Solar Telescope on ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects − [37, 38] and 460– 630 cm − regions [39]. In addition, ob-servations from Jungfraujoch in Switzerland (a higher, drier site than Kitt Peak) extendto longer wavelengths [40] and cover 250–630 cm − . At short wavelengths the CN RedSystem and the C Phillips System (A Π u − X Σ +g ) [41] can be seen, but the spectra aredominated by the strong first overtone and fundamental vibration-rotation bands of COnear 2.5 µ m and 5 µ m [42]. The Meinel bands (OH vibration-rotation bands) near 3 µ mare also strong and the OH pure rotational lines are prominent at long wavelengths [43].The vibration-rotation bands of CH can be seen at 3 µ m [33, 44].In the infrared, excellent high resolution solar spectra have also been recorded fromlow earth orbit by the ATMOS and ACE FTSs. The ATMOS instrument producedtwo solar atlases covering 625–4800 cm − at 0.01 cm − resolution [45, 46] and theACE atlas covers 750–4400 cm − at 0.02 cm − − [39], 1970–8640 cm − [50], 1925–3480 cm − [51], 4000–8640 cm − [52], 8900–15 050 cm − [53], and 15 000–23 000 cm − [54]. Pa-per copies are available from L. Wallace ([email protected]) and electronic copies fromftp://nsokp.nso.edu/pub/atlas/.All of the molecules seen in the photosphere intensify in the spectra of sunspots, withthe exception of C , which fades and is not obvious. The weak MgH B ′ Σ + − X Σ + [31, 55] transition makes its appearance in the near infrared, along with the A Π − X Σ + transition of AlH [56] near 425 nm and the B Σ + − X Σ + and A Π − X Σ + transitions ofCaH in the red [57]. The MgH lines can be used to determine Mg: Mg: Mg isotopicabundance ratios [55]. The lines of several electronic transitions of TiO [60] becomeextremely dense in the visible with the γ -bands (A Φ − X ∆) [58] and δ -bands (b Π − a ∆)[59] in the red and near infrared. The Sun and sunspots are remarkable sources forspectroscopy at 3000–6000 K, and the two TiO papers by Ram et al. [58, 59] nicelydemonstrate how laboratory and solar data (Figure 3) can be combined to give improvedspectroscopic constants.As in M-type stellar spectra the FeH F ∆ − X ∆ transition [61, 62] near 1 µ m andthe E Π − A Π transition [63] near 1.58 µ m are present in sunspots, but with a largeZeeman effect. The FeH F-X 0-0 band near 990 nm is called the Wing–Ford band in the ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath -1 ) I n t en s i t y ACE Solar Spectrum
Figure 1. The ACE solar spectrum with the intensity scale normalised to 1. Strong CO absorptionis seen near 2000 and 4000 cm − and OH pure rotational lines near 1000 cm − are clear. astronomical literature (see below). Interestingly the sunspot spectra were combined withlaboratory observations to derive rotational g -values for levels involved in some of thelow- J lines in the Wing–Ford band [64]. These g -values are useful in measuring magneticfields in cool objects. For hotter objects such as the Sun and sunspots the magnetic fieldstrength is obtained from magnetically-sensitive atomic lines (i.e. lines between levelswith large g -values) either by the observation of Zeeman splittings for large fields orfrom the polarization of the lines for weaker fields. In cooler stars and brown dwarfsthere are no useful atomic lines, so it has been proposed to use the Zeeman effect on thelines in the Wing–Ford band instead.The infrared spectra of sunspots display a great profusion of lines: in addition to theCO, OH, NH and CH molecules seen in the photosphere, SiO [65], HF [66], HCl [67], andH O [68, 69] appear. The fundamental and first overtone bands of SiO cover a substantialpart of the 10 µ m and 5 µ m regions [65], and H O has an amazing density of up to 50lines/cm − starting with the pure rotational region at the long wavelength limit andextending to nearly 7000 cm − [70] in the near infrared.An important advance in the spectroscopy of hot water occurred as a result of thedetection of water vapour in sunspots. At 5800 K, the Sun’s photosphere is too hot forwater to exist, but by 3900 K the concentration of OH and H O are equal. A large ctober 22, 2018 2:37 Dynamical Systems AstroReview-test
Molecular astronomy of cool stars and sub-stellar objects Figure 2. An image of a sunspot as seen with the Vacuum Tower Telescope of the National SolarObservatory at Kitt Peak. number of unassigned lines were noticed in two Kitt Peak sunspot atlases [39, 50]. It wassuspected that these lines were due to hot water but the available laboratory data wereinadequate to confirm this. New laboratory infrared emission spectra of hot water at1800 K were therefore recorded. Comparison of the laboratory emission spectra of H Oand the sunspot absorption spectra identified most of the unassigned sunspot lines asH O lines, but only a small fraction of the new water lines could be assigned quantumnumbers. This work proved that there was ‘water on the Sun’ but the line density wasso high that the spectrum seemed ‘unassignable’ by conventional techniques [68].We began a collaboration with the theoreticians Polyansky and Tennyson to applymore sophisticated approaches to the problem [69]. Through variational calculations ofthe energy levels using a high quality ab initio potential energy surface, Polyansky etal. [69] were able to assign most of the strong lines. The assignment method relies onthe smooth variation of errors and confirmation of tentative assignments by combinationdifferences.More recently, we have recorded a laboratory spectrum of water vapour at 3000 K byusing an oxy-acetylene torch as a source. The water emission in the 500–13 000 cm − spectral region was recorded with a high-resolution FTS [71]. Work on this 3000 K spec-trum of H O has just finished with the publication of the last paper in the series covering ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath
Figure 3. The 0-0 δ -band of TiO as (a) seen in the laboratory in emission as (b) seen in a sunspotin absorption and (c) absent in the solar photosphere [59]. Reproduced by permission of the AAS. the near infrared part [72]. This spectrum matches closely the conditions encounteredin the photospheres of late M dwarfs and sunspots. A paper on ‘monodromy’, that is,the change in the bending energy level pattern observed when the highly-excited watermolecule starts to sample linear geometries, has also been published [73]. In this paper,we identify vibration-rotation energy levels for the highly excited bending states 8 ν and9 ν above the barrier to linearity for the first time. In our analysis we included sunspotspectral data.An important application of hot water work is the calculation of molecular wateropacities for various cool objects. Reliable potential and dipole surfaces are needed tocompute the millions of transitions required to reproduce low-resolution infrared spectraof M-type stars and brown dwarfs. The latest water line list of Barber et al. [74] containsmore than 500 million lines and is recommended for the simulation of the spectral energydistribution of cool stars and brown dwarfs.Recently the solar abundances of C, N, O, and Ne have been revised downwards bynearly a factor of two based on the intensity of atomic and molecular lines through the ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects
4. K and M Stars
The Sun and particularly sunspots cover much of the temperature range spanned byK (4000–5200 K) and M (2400–3700 K) stars. Perhaps the best published spectrum isthat of Arcturus ( α -Bo¨otis), one of the brightest stars in the northern sky [83, 84, 85].Arcturus is a K1.5 IIIpe red giant star with a surface temperature of 4320 K (pe standsfor ‘peculiar emission’ because of the presence of emission lines in addition to the usualphotospheric absorption features). The infrared and near infrared atlas (0 . − . µ m) ofArcturus was recorded with the FTS that was associated with the 4-m Mayall Telescope[83] at Kitt Peak, the visible atlas (373–930 nm) with the 0.9-m coud´e feed telescopeand the coud´e spectrometer at Kitt Peak [84] and the UV atlas (115–380 nm) recordedmainly with the STIS instrument on the Hubble Space Telescope [85]. As expected, basedon the solar atlases, the same molecular features are present with the exception of C ,and the Lyman and Werner bands of H [86] appear in emission in the UV [85].M stars are particularly important because they are the most numerous type of starin our Milky Way galaxy, with 70% by number and 40% by mass [87]. Because they areso faint, it is only relatively recently that a full range of M dwarf spectra have becomeavailable [88, 89]. The visible and near infrared spectra of M-type stars are dominatedby TiO absorption bands (Figure 4) as discussed above for sunspots. In Figure 4, theterms ‘active’ and ‘inactive’ refer to magnetic activity which induces atomic emissionlines such as Balmer H α at 656 nm, and is associated with stellar rotation [90]. Noticethat astronomers have retained the old atomic notation with Na I referring to the neutralNa atom and Ca II to Ca + .The TiO 0–0 A Φ − X ∆ band head appears near 705.4 nm in the M1 spectra (3700 ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath α TiO5 K I Na I Ca IITiO TiOCaH VO TiOCaH Inactive M1Active M6CaOH TiO2TiO4CaH
Figure 4. Red and near infrared M dwarf spectra [89]. Reproduced by permission of the AAS.
K) and has nearly become saturated by M6 (2750 K) with weaker TiO features such asthe 0–1 band at 758.9 nm now present [91]. By M6 the B Π − X Σ − ′ Σ + − X Σ + ), CaH (B Σ + − X Σ + and A Π − X Σ + at 635 and 690 nm, Figures 4 and 5 ) and FeH (F ∆ − X ∆) are allprominent. Perhaps the most interesting new feature (Figure 4) in M spectra is ascribedto the CaOH e A Π − e X Σ + transition at 625 nm [94, 95]. In the infrared the overtonespectra of water appear more strongly than in sunspots for the late M’s (Figure 6).In fact it was in late M dwarfs that Wing and Ford [96] were the first to detect a mys-terious band near 991 nm at low resolution. The Wing–Ford band was later detected inS-type stars and in sunspots at higher spectral resolution [97]. Nordh et al. [98] identifiedthe Wing–Ford band as the 0-0 band of a FeH electronic transition by comparison withan unassigned laboratory spectrum that had a band head at 989.6 nm. The 1-0, 2-0, 2-1and 0-1 bands of this transition can all be identified in sunspot spectra. The spectra ofthe Wing–Ford band and the other bands are very irregular in appearance because ofmany overlapping branches with perturbed lines. Quantum chemistry predicts a largenumber of low-lying electronic states and their mutual interaction causes perturbationsthat appear as irregular patterns of lines. These ‘many-line spectra’ with no obvious pat- ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects Figure 5. Red and near infrared M9, L3 and L8 dwarf spectra [102]. Reproduced by permissionof the AAS. terns at first sight are characteristic of the electronic spectra of transition metal hydrides.After heroic efforts, the near infrared transition of FeH was shown to be a F ∆–X ∆transition and seven bands with v ′ , v ′′ ≤ ◦ C. More recently the lineintensities for the F ∆–X ∆ transition were obtained through ab initio calculation [62].The bands of CaH are particularly useful in identifying M subdwarfs that have reducedmetal abundances compared to our Sun [99]. TiO and VO which characterise M-starscontain two heavy elements (‘metals’ in the astronomical sense), while CaH has only asingle heavy element. If the metal abundances are low, then the CaH bands strengthenrelative to TiO, and the ratio of CaH to TiO band intensities can be used to identifysubdwarfs [99]. ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath
Figure 6. Near infrared M and L dwarf spectra [103]. Reproduced by permission of the AAS.
5. Brown Dwarfs
The discovery of the first brown dwarf Gl 229B by Oppenheimer et al. [100] in1995 was a momentous event and now hundreds of substellar objects are known(http://DwarfArchives.org/). Brown dwarfs are actually defined by mass because ob-jects with less mass than about 0 . M ⊙ = 79 M J (1 M ⊙ = 1047 M J , mass of Jupiter)are unable to fuse hydrogen in their cores but can still burn deuterium and lithium[101]. There is a similar deuterium burning limit at about 13 M J and the lithium limitis about 63 M J . Cool objects in the L and T classes, however, are classified primarilyby effective surface temperature, which controls the appearance of the spectra, and notby their difficult-to-determine mass. While there is certainly a correlation between massand surface temperature, the relationship is not simple because of the different possibleages of the objects. Low mass objects burn hydrogen, deuterium, lithium, etc. slowly andcan therefore have lifetimes of billions of years, and indeed some lifetimes are calculatedto be comparable to the age of the Universe. It is therefore possible for a small youngbrown dwarf to have the same surface temperature (and spectral class) as a larger oldlow-mass star that has been slowly cooling.The L class of objects is defined by the weakening of the VO and TiO metal oxide bands ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects Figure 7. Near infrared T dwarf spectra [107]. Reproduced by permission of the AAS. and the strengthening of the FeH and CrH metal hydride bands (Figure 5) [18, 102]. TheCrH A Σ + –X Σ + transition with a 0–0 band head at 861 nm first appears in late M’s(Figure 5) and is probably not present in sunspots [104, 105]. For later L’s, the absorptionbands of CrH and FeH fade and are replaced by infrared absorption of H O and CH overtone and fundamental vibration-rotation bands (Figures 6 and 7) [18, 106].The determination of surface temperatures of brown dwarfs is more complicated thanfor stars. In part the problem is due to their faintness and to difficulties observing inthe infrared with ground-based telescopes. As Figure 7 illustrates, the spectral energydistributions no longer resemble blackbody curves—molecular absorption has choppedthe spectral energy distributions into pieces. Surface temperatures therefore need tobe determined using simulations and these models are still relatively primitive withincomplete molecular opacities. The transition from M to L objects is particularly difficultto model because of the condensation of gases to form dust; the L to T transition is easier ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath to handle because the dust has settled out and has disappeared. In L-type objects particlescattering needs to be included in the simulation of spectral energy distributions in orderto match the observed extinction. Existing effective surface temperatures are ∼ ∼ ∼ ∼
800 K by T8[18].Brown dwarf masses are also difficult to measure. Evolutionary models predict thatwhile L’s could be stars or brown dwarfs, T’s are always brown dwarfs. One possibleindependent way to determine mass is from the surface gravity; astronomers are oftenable to determine the temperature, metallicity (composition) and gravity from high res-olution stellar spectra. Gravity affects the observed spectra by changing the thicknessand structure of the photosphere, which changes the appearance, for example, of thewings of lines. The first high resolution spectra are starting to appear [108, 109], but oneproblem is that all known brown dwarfs are rotating rapidly with velocities in excess of20 km/s, which corresponds to a spectral line broadening due to the Doppler effect ofabout 1 cm − near 1 µ m [110].The importance of high spectral resolution is illustrated for TiH. Opacity calculationspredict that TiH should be particularly abundant for late M-type subdwarfs [111]. In 2003Burgasser et al. [112] and Lepine et al. [113] classified two objects (2MASS 0532+8246and LSR 1610-0040, respectively) as metal-deficient L-type subdwarfs. In the Burgasseret al. paper [112] there is an ‘unassigned hydride’ band at 960 nm and another unassignedband at 940 nm. Both of these features are overlapped by a water overtone band in theEarth’s atmosphere and hot water absorption in the objects themselves. In a later paperon a third L-type subdwarf (2MASS 1626+3925) Burgasser [114] suggests that the featureat 940 nm might be due to the A Φ–X Φ transition of TiH [115]. Reiners and Basri [116]then recorded higher resolution spectra (resolving power, λ/ ∆ λ , of 31000) of two of thethree L-subdwarfs. They conclude that LSR 1610-0040 is not an L-type subdwarf buta peculiar slightly metal-deficient M-type dwarf with strong CaH bands and relativelyweak CrH and FeH features. The feature near 960 nm is due to a group of Ti lines andthere is no sign of the TiH lines near 940 nm in the high resolution spectrum of the Lsubdwarf 2MASS 0532+8246.For T-dwarfs the main contributors to the opacity are water, methane and ammonia.Cushing et al. [117] recorded a nice sequence of moderate resolution spectra of M, Land T dwarfs in the 0.6 to 4.1 µ m region with ground-based telescopes. These spectrashow beautiful methane features at 1.65 µ m (2 ν , first overtone of the C–H stretch,Figure 8) that begin to saturate at 3.4 µ m ( ν , C–H stretch fundamental) for a T5 dwarf[118]. Near 2.3 µ m the spectra also show the CO first overtone bands for L’s fade as thetemperature decreases towards the T’s and the dominant carbon-containing compoundbecomes methane (Figure 9). Water is present in all the L’s and strengthens towards theT’s (Figure 9). More recently spectra to longer wavelengths have become available fromthe Spitzer Space Telescope [119] and they clearly show the umbrella mode of ammonia ν at 933 cm − (10.7 µ m) in T dwarfs (Figure 10).Unlike the situation for water [74], reliable molecular opacities for hot methane and ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects Figure 8. Spectra of L dwarfs showing the FeH E-A transition and of T dwarfs with the methaneC–H first overtone band [117]. Reproduced by permission of the AAS. hot ammonia are not available. Hot emission spectra of methane at 800, 1000 and 1273 Kwere recorded to match the range of temperatures encountered in T dwarfs [118]. Thesespectra are not assigned so it is difficult to use them except at the temperatures at whichthey were recorded. Cushing et al. [117] have used our hot laboratory spectra to identifyfeatures due to methane in T dwarf spectra.The best existing database for methane and ammonia is HITRAN 2008 [120], whichis aimed at the calculation of infrared transmission of the Earth’s atmosphere at 300K. HITRAN is missing the hot bands needed for high temperature sources and is alsorather incomplete in the near infrared. New laboratory spectra for hot methane andammonia are clearly needed and some work is underway in our research group. There isalso steady progress on the calculation of the methane spectrum using ab initio methods[121], but the current predictions are far from spectroscopic accuracy; similar theoretical ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath
Figure 9. Near infrared L and T dwarf spectra showing CO first overtone bands [117]. Reproducedby permission of the AAS. work has been started on ammonia [122]. Hot ammonia is particularly significant for thenext cooler spectral class—Y brown dwarfs—that have surface temperatures less thanthe T’s [123].
6. AGB, S and C Stars
The spectra of S- and C-type stars are complicated because of the variety of molecularspecies that can form as the C/O abundance ratio increases as stars evolve off the mainsequence and start to burn He. S-type stars have C/O of about 1 while C-type stars haveC/O greater than 1 and are defined empirically by the presence of certain molecularbands in their spectra. These stars have surface temperatures that are roughly parallel ctober 22, 2018 2:37 Dynamical Systems AstroReview-test
Molecular astronomy of cool stars and sub-stellar objects Figure 10. Infrared spectra of L and T dwarfs with H O ν band near 6 µ m, CH ν band near8 µ m and NH ν band near 11 µ m [119]. Reproduced by permission of the AAS. to those of M stars and are believed follow the evolutionary sequence M-MS-S-SC-C,allowing for the possibility of intermediate MS and SC stages [124]. Values for C/O areabout 0.5 for M, 0.6 for MS, 0.8 for S and 1 for SC [125]. As discussed in the introduction,at the end of a star’s life on the main sequence stellar evolution proceeds through thered giant, AGB, planetary nebula and white dwarf stages. The empirical M-MS-S-SC-Csequence is therefore a consequence of stellar evolution and corresponds to the red giantand AGB part of stellar demise.S-type stars are traditionally classified by the presence of ZrO and YO bands in additionto the usual TiO bands of M-stars [124, 125, 126]. The heavy elements Y and Zr arebeyond the Fe abundance peak and are formed by s -process neutron reactions that arecharacteristic of stars that have left the main sequence. The classification notation usedis Sx,y or Sx/y, in which x is the usual 0 to 9 for surface temperature and y is a number ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath
Figure 11. Near infrared spectra of four S-type stars [136]. Reproduced by permission of theAAS. from 1 to 7 based on the relative intensity of TiO and ZrO bands (which is a proxy for theincreasing C/O ratio) [126]. A number of visible transitions of ZrO ( β system, c Π − a ∆; γ system, b Φ − a ∆ and B Π − X Σ + transition [124, 127, 128]) and YO (B Σ + − X Σ + and A Π − X Σ + transitions [129, 130]) are seen. With much of the oxygen tied up inCO, a number of unusual sulfur-containing molecules are able to form in S-type starsincluding TiS [131, 132, 133] and ZrS [134, 135] observed in the near infrared in, forexample, R Andromedae (R And, Figure 11 [136]).A high resolution FTS spectrum of the S-type star R Andromedae was recorded byRidgway et al. [137] in the 2400–2800 cm − region. Vibration-rotation lines of OH, NH,CH and HCl fundamental bands and the first overtone of CS [138, 139] were identifiedand later the fundamental band of SH [140, 141] was noted. To shorter wavelengths COand the Red System of CN are very strong in χ Cygni, an S-type Mira variable that has aregular pulsing stellar atmosphere [142]. Low resolution spectra from the Infrared SpaceObservatory (ISO) [125] suggest that HCN can be seen near 3 microns [143, 144], andrecently SiO and SiS were identified in Spitzer Space Telescope spectra near 10 microns[145]. ctober 22, 2018 2:37 Dynamical Systems AstroReview-test
Molecular astronomy of cool stars and sub-stellar objects Tc (the isotope formed by neutron reactions in AGB stars) has a half-life of 2 . × years and does not occur naturally on Earth. Tc, however, is an s -process element thatcan be identified through its atomic lines in intrinsic S stars (i.e. genuine AGB stars).Extrinsic S stars do not have Tc because it has all decayed away. It turns out that allextrinsic S stars are binary with a white dwarf as a companion. Apparently the heavy s -process elements such as Y and Zr in extrinsic S stars were transferred through massloss during the companion’s AGB phase.Carbon stars have perhaps the richest of all stellar spectra and this has caused consid-erable confusion in their classification. Traditionally C stars are identified by the strongvisible absorption of the C Swan system, CN Red and Violet Systems and the CH A-Xtransition [147, 148, 149]. Carbon stars can also display the Merrill–Sanford bands dueto the e A B − e X A transition of SiC (origin band near 497.7 nm [150]) and the cometsystem of C ( e A Π u − e X Σ +g transition near 405.2 nm [151]). The simple approach ofclassifying carbon stars by their surface temperature and the amount of carbon (as mea-sured by the strength of the C Swan bands) is not very successful because of the widerange of objects that have C/O greater than 1. The surface temperatures of C stars arenotoriously difficult to determine. The current system divides C stars into three mainsub-classes R, N and CH (denoted as C-R, C-N and C-H), and then further categoriseseach of these by temperature, strength of C , peculiar carbon isotope ratios and lumi-nosity [148]. The R type is hotter and has no Ba lines from the s -process, while thecooler N-type has enhanced heavy elements with strong blue absorption. The CH typehas strong CH absorption and the J-subtype also has strongly enhanced C abundances,with C/ C ratios as high as 2 as compared to the solar value of 92. Isotopic abun-dances show great deal of variation in astronomy and often provide important clues tothe evolutionary history of the object. CH carbon stars are believed to be part of binarysystems with white dwarfs (like extrinsic S stars) and their anomalous abundances aredue to mass transfer from the other star [152].The near infrared spectra of carbon stars are dominated [153] by the CN Red System,the Phillips and Ballik–Ramsay (b Σ − g − a Π u [154]) systems of C and CO overtonebands. The vibration-rotation bands of HCN and C H appear in the 3 µ m region andto slightly longer wavelengths CH, NH and CO fundamentals and the CS first overtonecan be seen in both ISO spectra [155] and at higher resolution in FTS spectra [137, 156].In the ISO spectra [155] the fundamental band of CS and the first overtone of SiS aredetected near 7 µ m plus the ν bending mode of HCN at 14 µ m and the ν bendingmode of C H at 13.5 µ m [157]. The detection of C has also been suggested using lowresolution ISO [158] and Spitzer spectra [159, 160].It is also possible to have oxygen-rich AGB stars and their infrared spectra typicallyshow OH, H O, SiO, CO, CO , SO , HCl and HF, as expected from their compositionand the surrounding cloud of molecules from mass loss [161, 162, 163]. ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath
7. Extrasolar Planets
The first extrasolar planet—a ‘hot Jupiter’ orbiting around the star 51 Pegasi—wasdiscovered by Mayer and Queloz in 1995 [164], the same year the first brown dwarf wasobserved [100]. The parent star is classified as G2 V and is very similar to the Sun, butthe 51 Pegasi b planet is very strange indeed. (Planets are named using the parent starand lower case letters b, c, d, and so forth in order of discovery.) 51 Peg b has a massof about 0.5 M J , but is located at 0.05 AU (1 AU is the mean Earth-Sun distance of1 . × m) and has an orbital period of 4.2 days. In essence it would be as if Jupiterwere to be transported so it was 7 times closer to the Sun than Mercury in our SolarSystem. The composition of 51 Peg b is expected to be similar to that of Jupiter butwith a surface temperature of about 1300 K rather than about 125 K for Jupiter.Almost all of the hundreds of extrasolar planets (or exoplanets, seehttp://exoplanet.eu/) have been detected by observing periodic Doppler shifts inthe spectrum of the parent star. A star and a planet orbit about a common centre ofmass and this motion causes the parent star to periodically move away and toward theobserver. For example, the Sun-Jupiter system would have a periodic Doppler shift of13 m/s for lines in the Sun [27]. Detection sensitivities are currently better than 3 m/s,which corresponds to a frequency shift of about 5 MHz for the Na D line. Interestingly,most of the Doppler shift observations view the star through a temperature-stabilisediodine cell (as a frequency reference) and record a high resolution visible spectrum. Itis not possible to determine the inclination angle of the orbital plane from the Dopplereffect, but these observations give the orbital radius, eccentricity of the orbit and a lowerlimit for the mass of the planet (as long as the stellar mass is known). The Dopplershifts are largest for large planets close to the parent star so there is a selection effectthat favours the detection of hot Jupiters. Given a few technical improvements theDoppler shift method should be able to detect Earth-like planets.For extrasolar planets, it is possible that the orbital inclination (the angle between theEarth-star vector and the perpendicular to the star-planet orbital plane) is close to 90 ◦ .The planet can then transit the star and be detected by the small decrease in light as theplanet passes in front of the star. The hot Jupiter HD 209458b was the first transitingplanet observed with a dip in light intensity of about 1.5% [165]. This type of precisionphotometry is best done from orbit and the Corot (http://smsc.cnes.fr/COROT/) andKepler missions (http://kepler.nasa.gov/) are currently searching for Earth-like planetsby their transits. The combination of Doppler and transit data allows for a rather com-plete description of the planet including orbit inclination, planetary mass, radius anddensity.The technique of ‘transit spectroscopy’ allows the detection of molecular absorptionsin exoplanets. The idea is simple: the effective size of a planet with an atmospheredepends on the wavelength because the planet appears bigger at a strongly absorbingwavelength than at a wavelength for which the atmosphere is transparent. By measuringvery precisely the size of the dips in the stellar radiation during transit as a function ctober 22, 2018 2:37 Dynamical Systems AstroReview-test Molecular astronomy of cool stars and sub-stellar objects µ m range. HD 189733b is a hot-Jupiter planet in a 2.2 day orbitaround a bright K2 V primary star. A model atmosphere of mainly molecular hydrogenwith a water relative abundance of 5 × − and a methane abundance of 5 × − wasneeded to match the observed wavelength dependence of the transit dips. They used theBT2 [74] linelist for water and a combination of HITRAN [120] and Nassar and Bernath[118] for methane.More recently the ‘emergent flux’ from the same planet was directly detected [1657]with a similar instrument configuration as used for transit spectroscopy [166]. The NIC-MOS instrument on Hubble was used again for imaging spectroscopy with a grism (agrating ruled onto a prism inserted in the field of view of an infrared camera) that gavea resolving power of 40 in the 1.4–2.5 µ m range. In essence Swain et al. manipulate thespectra recorded just before the planet disappears behind the star (i.e. star plus planet)and spectra recorded during occulation with the planet behind the star (i.e. star only) toobtain the emission spectrum of the planet alone. The planetary flux contained modula-tions that required the addition of H O, CO and CO to their model atmosphere. Theinterpretation of such spectra are not straight forward because the molecular bands couldappear in absorption or emission or both, depending on the details of the atmosphericpressure-temperature height profile and the composition of the different atmospheric lay-ers. The non-detection of methane is explained as being due to the different atmosphericregions sampled by emission spectroscopy (dayside emission from higher pressure andtemperature regions) as compared to transit spectroscopy (sampling of lower pressurecooler outer regions in the terminator between night and day).
8. Molecular Opacities
The spectra of cool objects are rich in molecular absorption features, which presents amajor difficulty in the calculation of model atmospheres needed to simulate the spectralenergy distribution functions. Compared to atoms, molecules have many more energy lev-els and hundreds of millions of absorption lines are needed for molecular opacities. It isnot feasible to obtain millions of line parameters from laboratory observations alone: theymust be provided by theory. Yet the purely theoretical calculation of molecular opacitiesis also not satisfactory because, except for molecular hydrogen, ab initio quantum chem-istry is not yet sufficiently accurate. In other words, laboratory measurements alone donot provide sufficient lines while purely theoretical calculations do provide enough lines,but not with enough accuracy. The solution to this problem is to extend laboratorymeasurements with theory to provide the required molecular opacities. In essence, thestrongest lines seen at high resolution come from laboratory data, but the millions ofweaker lines that provide a kind of ‘continuum’ absorption come largely from theory. ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath
The calculation of molecular opacities has been recently reviewed by Sharp and Burrows[168].Our approach to the calculation of molecular opacities for the electronic transitions ofmetal hydrides such as FeH illustrates the contributions chemical physics can make inastronomy. The simulation of these spectral energy distributions require spectroscopicline parameters (positions, intensities and pressure-broadening parameters) to be usedin a model atmosphere [169]. The generation of the required molecular opacities is notan easy task for molecules such as CrH, FeH and TiH. The assignment of perturbedlaboratory spectra are difficult and require considerable patience using combination dif-ferences. The use of just laboratory data, however, is not satisfactory for astronomicalpurposes because even for metal hydrides tens of thousands of lines contribute to theobserved stellar and substellar spectra. The vibrational and rotational levels generallyneed to be extended to higher v’s and J ’s than observed in the laboratory. This canbe done empirically or by using the predictions of ab initio quantum chemistry. Purely ab initio opacities, however, are not satisfactory because the calculated line positionsare not accurate enough. A judicious combination of experiment and theory works bestto cover a wide range of v and J . Minor isotopes and satellite branches should also beincluded, usually from theory, because when absorption from the main lines saturate,the weaker satellite and minor isotopologue lines become important.Line intensities are also required and the best approach is to measure the radiativelifetimes for a few lines by, for example, laser spectroscopy. The transition dipole momentfunction can be computed by ab initio quantum chemistry, but typical errors for state-of-the-art calculations are 10-25%. For example, our prediction of the radiative lifetime ofthe A Σ + v=0 level of CrH was 0.75 µ s [104] and a subsequent experimental measurement[170] yielded a value of 0.939 µ s, some 25% larger. Perhaps the most reliable approachis to compute the ab initio transition dipole moment function and then scale it withan experimental measurement to match the observations. Theory is thus being usedto extend an experimental value to cover a larger range of vibrational levels. Finally,pressure-broadening parameters can also be determined by experiment or theory, butthey are difficult to measure or compute so generally some reasonable values are justassumed [105].The first step in obtaining molecular opacities for CrH, FeH and TiH is to use theobserved lines for the A Σ + –X Σ + (CrH [104]), F ∆–X ∆ (FeH [41]), A Φ–X Φ (TiH[115]) and B Γ–X Φ (TiH [171]) transitions in fits to obtain the usual spectroscopicconstants for each vibrational level. These constants are obtained by deweighting theperturbed lines, which is particularly difficult for the heavily perturbed FeH bands. Thenext step was to carry out ab initio calculations of molecular properties using multiref-erence configuration interaction (MRCI) method with the MOLPRO suite of programs[62, 104, 111]. Large atomic basis sets were used and scalar relativistic effects were in-cluded. In the initial multireference part of the calculation, the valence electrons weredistributed among the valence orbitals (‘active space’) to generate a large number ofSlater determinants that were treated equally in a CASSCF (Complete Active Space ctober 22, 2018 2:37 Dynamical Systems AstroReview-test
Molecular astronomy of cool stars and sub-stellar objects B v ) by solution of the one dimensional radial Schr¨odinger equation. This wasparticularly important for TiH [111] because only the 0-0 vibrational bands are availablefor the A-X and B-X electronic transitions. For TiH, therefore, the vibrational constantswere taken from ab initio calculations for each electronic state. The vibration-rotationenergy levels were calculated (including the effects of spin-orbit and spin-spin coupling)for FeH [62] and TiH [111] for v’s from 0 to 4 or 5 and rotational levels typically up to N of about 50. In our first effort on CrH [105], we covered only up to v=3 and about N =40, which should be extended to higher v and N . These tables of energy levels areadjusted to contain the experimental term values derived directly from the observationsif they are available, otherwise calculated values are used. In this way, the experimentalline positions are reproduced by the energy levels.In the next step, all possible transitions are computed from the tables of energy levels,even the weak satellite lines and weak bands not seen in the experiments. Each calculatedline requires an intensity so an Einstein A ij value was calculated. The starting point wasthe transition dipole moment for each electronic transition calculated from the electronicwavefunctions. The vibrational wavefunctions were then used to calculate the Einstein A value for each vibrational band. The Einstein A value (in s − ) for each line wasthen calculated using the formula A = A v ′ v ′′ HLF/ (2 J ′ + 1), in which HLF is a H¨onl–London factor (for rotation) and A v ′ v ′′ is the Einstein A value for the v ′ − v ′′ band. TheH¨onl–London factors were obtained from the Hund’s case (a) expressions (which had tobe derived for the ∆– ∆, Φ– Φ and Γ– Φ cases) and the rotational wavefunctionsobtained during the calculation of the energy levels. The line strength [1] of each lineis most convenient in the form of an integrated cross-section R σdν in units of cm s − molecule − . The integration over frequency is just to eliminate the line shape function.The integrated cross-section for a line is calculated from the Einstein A by Z σdν = 18 π ˜ ν Q A (2 J ′ + 1) exp( − E ′′ /kT )(1 − exp( hν/kT )) (2)with ˜ ν in cm − ; Q is the internal partition function. As the partition function appears inthe line strength function, we also re-evaluated the thermochemistry for each moleculeusing the best estimates of the dissociation energies. We computed the partition functionusing estimated spectroscopic constants for all of the low-lying spin components andelectronic states. The correct evaluation of the partition function is a frequent problemin astronomical applications and the simple rigid rotor, harmonic oscillator expressionsthat are approximately valid at 300 K, are rarely reliable at high temperature.The new molecular opacities and thermochemistry for CrH, FeH and TiH have been ctober 22, 2018 2:37 Dynamical Systems AstroReview-test P. F. Bernath incorporated into a spectral synthesis code by Burrows [62, 105, 111]. A comparison ofthe observed spectrum of the L5 brown dwarf 2MASS-1507 and the spectral simulation(including FeH and CrH) was carried out [62]. The agreement was reasonable, consideringthat L dwarfs are hard to model because of the presence of dust in their atmospheres.More recent comparisons with high resolution spectra are not so favourable [108, 109]and it is clear that many of the line positions and intensities will need to be adjustedbased on experimental observations.
9. Conclusions
Astronomy of the cool Universe is the study of molecules. As illustrated in this review,the tools of modern chemical physics can be used to great advantage in astrophysics.What is also evident is that astronomy in turn provides some unique environments formolecules and for the study of molecular processes that are rarely encountered in thelaboratory. A remarkable early example was the observation of only the predissociated lines of the A Π − X Σ + transition of AlH in emission in the spectrum of the MS-type variable star χ Cygni [172]. These AlH lines are not seen in laboratory emissionspectrum because of tunnelling through a potential barrier in the A state, but appearthrough inverse predissociation in the stellar atmosphere as Al and H atoms recombine.
Acknowledgements
Support from the UK Engineering and Physical Sciences Research Council (EPSRC)and the NASA laboratory astrophysics program is appreciated. I am grateful for thecomments on the manuscript provided by N. Allen, R. Hargreaves, J. Tandy and M.Cushing.
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