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over the past twenty years , discoveries of planets , stars and substellar objects have demonstrated the enormous diversity of astrophysical bodies in the universe . thanks to modern techniques and technology , it is now possible to study the atmospheres of these objects and retrieve some knowledge of their composition , structure and dynamics . however , these are extremely complex systems to model and accurate observations are still difficult to perform . in particular , it is crucial for the correct characterisation of these atmospheres that complete and accurate descriptions of the molecules that comprise them are available . here phosphine , or ph@xmath6 , is considered . phosphorus is the one of the most abundant chemically reactive volatile elements in a solar type system ( with s , after h , c , n and o ) . although phosphorus has considerably smaller cosmic abundances than h , o , c or n , it is predicted to have an important role in atmospheric chemistry and dynamics . phosphorus is not particularly common in the universe but it is ubiquitous and is important for most essential biochemical functions . due to its role as biogenic particle , phosphorus could potentially be used in the search for extinct or extant life in other planets @xcite .    a large fraction of the existing phosphorus in various astronomical environments is expected to be found in the form of phosphine , or ph@xmath6 @xcite . phosphine is an extremely toxic , semi - rigid , relatively stable , oblate , symmetric - top molecule , and has so far been detected in the lower troposphere of the earth , the atmospheres of jupiter and saturn , and in the carbon star envelope irc + 10216 @xcite . partially due to the lack of strong absorption from ch@xmath7 , the 5  @xmath2 m spectral window is a region of low opacity in jupiter , saturn and the earth s atmosphere . alongside other molecules ( co , geh@xmath7 , ash@xmath1 ) , ph@xmath1 is partly responsible for the continuum opacity in this region and has detectable absorption bands @xcite , specifically the @xmath8 overtone bending band . in jupiter , phosphorus is found at approximately tropospheric solar abundances ( 1.1  ppm ) in the form of phosphine , and is over four times more abundant in saturn ( 4.5  ppm ) , also as phosphine @xcite . this agrees with models of core accretion that expect saturn to have a considerably larger fraction of ice to gas than jupiter . in both planets , this abundance of a disequilibrium species like phosphine at observable levels of the atmosphere reflects both a large reservoir in deep regions of the planets and the strength of the convective transport of the molecule .    in local thermochemical equilibrium ( lte ) , p@xmath9o@xmath10 would be expected to dominate the upper atmospheres of planets with approximate solar abundances . however , almost no p@xmath9o@xmath10 is found in these environments because phosphine quenching and rapid vertical mixing from regions where ph@xmath1 is dominant leads to high disequilibrium abundances . this quenching occurs because timescales for the conversion of ph@xmath6 to p@xmath9o@xmath10 are much larger than the convective timescales , so the production of p@xmath9o@xmath10 is kinetically inhibited @xcite . disequilibrium chemistry is expected to lead to phosphine being orders of magnitude more abundant than predicted by equilibrium models , both for environments where t @xmath11 and at the uppermost atmosphere of most substellar objects @xcite . the thermal decomposition of phosphine at high temperatures has been studied for a long time , starting with @xcite . recently @xcite discussed at length the pressure and temperature parameters at which phosphine is expected to be found in solar composition and lte environments . at 1 bar , phosphine is predicted to be a dominant phosphorus carrying molecule in environments with temperatures up to about 1500 k , and it is expected to contribute to the composition of atmospheres up to about 2500 k if the pressure is above 3 bar .    the detection of phosphine can therefore be used as a chemical probe for deep layers of both jupiter and saturn s atmosphere , as it is only present at the top layers through vertical mixing . analysis of future observations of jupiter from nasa s texes , nasa s juno and esa s juice will require accurate data on phosphine , and past observations of saturn from cassini / vims and cassini / cirs will gain from further understanding its spectrum @xcite . suspected inaccuracies found in regions of the existing phosphine data may be behind misinterpretation of previous astronomical data @xcite . additionally , juno will cover the full latitude and longitude of jupiter and its analysis of the polar atmosphere of jupiter should confirm a depletion of phosphine in the polar vortices analogous to saturn s @xcite . titan has also been predicted to contain phosphine , but spectrum recorded with cassini cirs failed to detect any , putting an upper limit of 1 ppb on the phosphine abundance of its atmosphere @xcite . similar unsuccessful detections of phosphine in neptune and uranus suggest that the abundance of phosphorus on these planets is sub solar @xcite , with an upper limit of 0.1 times solar p / h abundance . the existence of phosphine outside the solar system has recently been confirmed by @xcite in the carbon star envelope irc + 10216 , with an abundance of @xmath12 relative to h@xmath13 . this was done using the hifi instrument on board herschel . together with hcp , ph@xmath6 is one of the major phosphorus carriers in the inner circumstellar regions . there have been multiple predictions of phosphine in many other astrophysical environments , but its presence and formation scenarios remain poorly understood and none has been found outside the solar system other than the aforementioned discovery of circumstellar phosphine in irc + 10216 . this is due to a variety of factors , including the sparsity of fundamental data which this work is rectifying . below are some of the expectations for further phosphine detection . a particular region of interest is the 4.1 - 5.1  @xmath2 m window , which is found to be an interval of very low opacities in both jupiter and saturn . it is therefore expected that detection of ph@xmath1 in this region could be used as a marker for vertical convection and a tracer for tropospheric dynamics in the upper atmospheres of other astronomical bodies , namely hot jupiters and brown dwarfs .    in y dwarfs , with @xmath14  k , phosphine should exhibit a strong feature in the mid - infrared at 4.3  @xmath2 m @xcite , where it is predicted to be the dominant source of opacity . t dwarfs , with @xmath15  k , will mostly be dominated by other molecules ( e.g. h@xmath16 , nh@xmath1 , ch@xmath7 , co , h@xmath16o and co@xmath16 ) but phosphine can still have a significant contribution to the shape of the spectrum . the nirspec near - infrared spectrograph on jwst will be able to collect spectra in the 2.9 - 5  @xmath2 m region with sufficient sensitivity to detect the presence or absence of phosphine , particularly for slightly cooler y dwarfs with @xmath17  k @xcite . phosphine is predicted to be the dominant phosphorus molecule in cool t dwarfs like gliese 229b where it is expected to carry all the phosphorus in the atmosphere to the top layers , with approximately 0.6 ppm . ph@xmath1 should be detectable ( for resolutions higher than 1.2 @xmath4 ) in the 4.45 - 5.40 @xmath2 m spectral window of gliese 229b , particularly the 4.3  @xmath2 m feature @xcite . models estimate that , for regions where @xmath181155 k , the major phosphorus carrying gas in gliese 229b is phosphine , with rapid vertical mixing quenching its destruction @xcite . as the temperature rises , ph@xmath6 is converted to p@xmath9o@xmath10 , but it should still be present at observable heights .    in hotter environments , like hd209458b and l dwarfs , where phosphorus equilibrium chemistry is approached , the phosphine abundances decrease significantly to about 50 ppb @xcite . it is still possible to detect phosphine in these atmospheres , but higher resolution is required to distinguish its features from that of neighbouring co bands @xcite . however , phosphine is expected to be the dominant phosphorus carrying species at the observable atmosphere of hot t dwarfs and cool l dwarfs , with effective temperatures between 1000 and 1400  k @xcite . there are still disequilibrium effects that are not completely understood . for example , observations of saturn s upper troposphere found that phosphine abundances decreased with depth @xcite , contradicting the proposal that phosphine is dredged up through vertical mixing from deeper layers of the atmosphere . this depletion is not understood , as there is no known formation mechanism for phosphine at the upper levels of saturn s atmosphere that could lead to the abundances observed . suggested explanations for this inconsistency are a poor understanding of the aerosol opacity in the vims observations and intensity uncertainties in the molecular data . future detections of phosphine can only be achieved by accurately modelling these atmospheres . this requires an extensive knowledge of the temperature dependent spectrum of phosphine , which can only be established with a comprehensive line list . there are multiple sources of phosphine data @xcite , both experimental and theoretical , which are further described in our previous paper on room temperature phosphine @xcite . additionally , a recent paper by @xcite improved the experimental phosphine spectrum for the 4.085.13  @xmath2 m region , which , as mentioned above , is of particular importance due to it being an interval of low opacity in gas giants and brown dwarfs @xcite . most of these experimental sources have already been incorporated in the hitran database @xcite and collectively contain less than 30  000 lines , and no wavelength coverage shorter than 2.7  @xmath2 m . despite these efforts , no complete line list for hot phosphine exists in the literature . the line lists mentioned above only cover low values of rotational excitations , a small number of bands , and some regions are missing altogether . often , contamination of gas samples affects the measured intensities @xcite , and this can be an effect that is hard to accurately compensate for . it is not unusual for experimental data with extremely accurate line positions to have intensity uncertainties well above 10% . additionally , all the experimental datasets mentioned above are designed to be used only at room temperature and below . consequently , they are insufficiently complete to be appropriate for use in the characterisation of atmospheres of any astronomical bodies at higher temperatures . a theoretical line list for phosphine was previously computed by us @xcite , henceforth syt . however , although syt contains many orders of magnitude more lines than any previous phosphine line list ( 137 million transitions between 5.6 million energy levels ) , it too was only designed to be accurate for temperatures below 300  k , making it unsuitable for most astronomical studies . since hitemp @xcite , hitran s high - temperature database , does not include phosphine , salty is the first line list suitable for modelling phosphine spectra in environments up to 1500  k. the completeness and coverage of the salty line list makes it particularly suitable for studies of non - lte environments . the current work is performed as part of the exomol project . this project aims to provide line lists of spectroscopic transitions for key molecular species which are likely to be important in the atmospheres of extrasolar planets and cool stars ; its aims , scope and methodology are summarised in @xcite . the salty line list builds on previously released ones for polyatomic hydrides such as water @xcite , ammonia @xcite , formaldehyde @xcite , and methane @xcite . finally we note that energy levels generated for this work have been used as part of a study to compute thermodynamic properties of phosphine and ammonia , including its partition function , for temperatures up to 6000  k @xcite . in the following ph@xmath1 and phosphine will refer to the main isotopologue @xmath0ph@xmath1 , since @xmath0p is the only non - synthetic , stable isotope of phosphorus . salty is a catalogue of transitions , each characterised by a frequency , its lower and upper energy level , einstein coefficient and quantum numbers . together these fully describe the spectrum of the phosphine molecule within the frequency range 0  10 000  @xmath4 , or wavelengths longer than 1  @xmath2 m . it contains 16  803  703  395 transitions between 7  480  690 energy levels below 18  000 @xmath4 , with rotational quantum number @xmath19 values up to 46 . the highest energy state considered is 18  000  @xmath4 above the zero - point energy ( 5  213.9280  @xmath4 ) for phosphine , as the intensity of transitions to higher energy levels is too weak to be important , even at temperatures of 1500  k. consequently , to ensure that the line list is complete within the frequency range 0  10  000  @xmath4 , the highest lower energy state considered is 8  000  @xmath4 . all transitions are within the ground electronic state of phosphine , since the first excited electronic state is above the dissociation limit of the molecule . the strongest salty transition has an einstein-@xmath20 coefficient of @xmath21 s@xmath22 while the weakest lines go down to @xmath23 s@xmath22 . in non - lte environments even extremely weak lines can play an important role in the shape of a spectrum . this is the reason behind including transitions with extremely weak absorptions in salty . the final line list is presented in the exomol format @xcite , with a transition file ordered in increasing transition frequency and an energy file . the former contains a description of each transition by its upper ( final ) and lower ( initial ) energy level reference numbers ( @xmath24 and @xmath25 ) , as well as the electric dipole transition probability represented as an einstein coefficient @xmath26 in s@xmath22 . using this information , the line intensity of each transition can be calculated for any given temperature . the latter connects each index with the description of the corresponding energy level . each energy level is described by the quantum numbers associated with the molecular group symmetry @xcite , @xmath27(m ) for ph@xmath1 and total angular momentum @xmath19 . the quantum numbers for xy@xmath1 molecules are quite complicated and have recently been discussed in detail for ammonia by @xcite . our ph@xmath1 quantum numbers follow the same general principles but are somewhat simpler since we neglect the possibility of a tunnelling mode . each energy level is described by the following quantum numbers : @xmath28 where @xmath29 . here the vibrational quantum numbers @xmath30 ( symmetric stretch ) , @xmath31 ( symmetric bend ) , @xmath32 ( asymmetric stretch ) and @xmath33 ( asymmetric bend ) correspond to excitations of , respectively , the @xmath34 , @xmath35 , @xmath36 and @xmath37 modes . the doubly degenerate modes @xmath36 and @xmath37 require additional quantum numbers @xmath38 and @xmath39 describing the projections of the corresponding angular momenta ( see @xcite ) . the vibrational quantum number @xmath40 , characterizes the coupling of @xmath41 and @xmath42 . the projection of the total vibrational angular momentum @xmath43 is included to reduce ambiguity in the description of the energy levels , as it was in syt @xcite . @xmath44 , @xmath45 , and @xmath46 are , respectively , the symmetry species of the rotational , vibrational and total internal wave - functions in the molecular symmetry group @xmath47(m ) , spanning @xmath48 , @xmath49 and @xmath50 , where @xmath50 is two - fold degenerate . @xmath19 is the total angular momentum and @xmath51 is the projection of the total angular momentum on the molecule fixed axis @xmath52 . these twelve quantum numbers reduce ambiguity to the assignment of the energy levels . however , only @xmath19 and @xmath53 are rigorous ; at higher energies , energy states can not necessarily be assigned unambiguous quantum labels . apart from the quantum numbers we also provide the largest eigen - coefficient used to produce the theoretical assignment , see , for example , @xcite . since ph@xmath1 transitions obey the strict selection rules @xmath54 , and @xmath55 , no higher @xmath19 values were considered because @xmath56 is the highest value of @xmath19 for which there are eigenvalues exist below 8 000  @xmath4 , which is the highest lower energy threshold used in salty . excerpts from the energy and transition files are given in tables  [ t : energy - file ] and  [ t : transit - file ] , respectively , with seven additional columns giving trove quantum numbers which are described in the supplementary data and by @xcite . as per the exomol convention , these are named salty.transitions and salty.states . the complete line list is freely available and can be downloaded from the strasbourg data centre , cds , via ftp://cdsarc.u-strasbg.fr/pub/cats/j/mnras/ or from the exomol website , www.exomol.com . the website also offers the opportunity to download cross sections @xcite . .[t : energy - file ] extract from the salty energy file . [ cols="^,>,>,>,>,>,>,>,>,>,>,>,>,>,>,>,>,>,>,>,>,>",options="header " , ]     using the equations above and the present line list , multiple cross - sections were simulated for ph@xmath1 . figures  [ ph3_overview ] and  [ ph3_zooms ] illustrate the temperature dependence of phosphine for @xmath57 = 300 , 500 , 1000 , 1500 and 2000 k. it can be seen that the spectra at higher temperatures have less features and a loss of sharp @xmath58-branches . figure [ ph3_zooms ] , part * c * , covers the wavelength region 3.8  5.1 @xmath2 m which , as mention above , is of particular importance for the spectral characterisation of brown dwarfs and gas giants . [ f : nlines : temp ] demonstrates how the density of lines per an absorption intensity @xmath59 unit changes with temperature , covering the whole wavenumber range 010  000 @xmath4 . as the temperature rises , the number of intense lines increases but the range of intensities in the spectrum becomes narrower . the gaussian - like intensity distributions peak at @xmath60 = @xmath61 , @xmath62 , @xmath63 , and @xmath63 for @xmath57 = 298 , 500 , 1000 , and 1500 k , respectively . this is different from the intensity distribution found for ch@xmath9  by @xcite , where the proportion of strong lines was found to be much larger . @xcite offers a detailed comparison of syt to the existing experimental data , where it was found that it replicates very well the observed phosphine spectra at room temperature , with a maximum rms deviation from cdms @xcite of 0.076 @xmath4 for the rotational spectrum and of 0.23 @xmath4 from hitran @xcite . as can be seen from fig . [ hitran_comparison ] , the salty line list is also in excellent agreement with hitran ( and incorporated cdms data ) , and it is expected that salty will have slightly lower rms deviations from experiment at this temperature . the most recent cdms update @xcite contains a very comprehensive description of the pure rotational band of phosphine . figure [ cdms ] demonstrates that salty is in excellent agreement with the cdms data . the transitions in the bottom left box shows a deviation of approximately 0.01 @xmath4 , while the right most box , at higher wavenumbers , shows a deviation of approximately 0.04 @xmath4 . the apparent intensity disagreements with hitran occur because of an overestimation of the intensity of some of the degenerate @xmath64 transitions which are in such close proximity that they have been perceived as one doubly strong transition in the experimental data . this has been partially resolved by @xcite , who corrected these intensities for the region 1950 to 2450 @xmath4 . the bottom left box in figure [ hitran_comparison ] includes this data , and it can be seen salty is in much better agreement with it than with the hitran data . we recommend that the @xcite data should be included in the next release of hitran . the data in hitran are generally very accurate for room temperature simulations . however , if the current hitran database is used to simulate high temperature spectra , the differences become much more striking , as can be seen in fig . [ hightemp_overview ] . the only available data above 300 k comes from the pacific northwest national laboratory ( pnnl ) who provide cross - sections for ph@xmath6 up to temperatures of 323 k @xcite . comparisons with salty for @xmath65  c , or 323 k , can be seen in fig . [ f : pnnl ] . the pnnl data is approximately @xmath66 weaker than salty s , but both are otherwise in good agreement . given its larger density and coverage , it is recommended that salty is used to simulate cross - sections , even at low temperatures . an accurate and comprehensive line list for phosphine is presented , which has been called salty . it contains 16.8 billion transitions between 7.5 million energy levels and it is suitable for simulating spectra up to temperatures of 1500  k.    its only limitations are : upper states with energies above 18000  @xmath4 are excluded , and there is an effective short - end wavelength cut - off of 1  @xmath2 m , which is an unimportant region for ph@xmath6 . salty improves on the previous room temperature phosphine line list syt in terms of the size of the basis set , corresponding refined potential energy surface and increased spectral range . it is therefore recommended that salty is used for all applications , even at low temperatures where syt would provide reasonable results . the tunnelling effect present in ammonia is predicted in phosphine but has yet to be observed in phosphine @xcite , due to its much higher inversion barrier ( 12  300 @xmath4 ) . this tunnelling effect is not considered here , but rough preliminary calculations have predicted the position , size and intensity of transitions from split energy levels . further work on this effect will be published elsewhere . the salty line list is presented as the latest in a series of molecules as part of the exomol project , which aims to provide comprehensive line lists for every molecule relevant to the characterisation of the atmospheres of cool stars and exoplanets . salty is freely available online in full or filtered by wavelength and intensity , from the exomol website . the line list in its entirety is very large but can be made more manageable by using cross sections @xcite ( available at exomol ) or @xmath67-coefficients @xcite . this work was supported by the erc advanced investigator project 267219 . the research made use of the dirac@darwin , dirac@cosmos and the emerald hpc clusters . dirac is the uk hpc facility for particle physics , astrophysics and cosmology and is supported by stfc and bis . the cosmos shared memory system at damtp , university of cambridge operated on behalf of the stfc dirac hpc facility . this equipment is funded by bis national e - infrastructure capital grant st / j005673/1 and stfc grants st / h008586/1 , st / k00333x/1 . the emerald high performance computing facility is provided via the centre for innovation ( cfi ) . the cfi is formed from the universities of bristol , oxford , southampton and ucl in partnership with stfc rutherford appleton laboratory . we thank james briggs ( cosmos ) and cheng liao ( sgi ) for their help with the plasma eigensolver . tennyson j. , hill c. , yurchenko s.  n. , 2013 , in aip conference proceedings , vol . 1545 , 6@xmath68 international conference on atomic and molecular data and their applications icamdata-2012 , aip , new york , pp .
a comprehensive hot line list is calculated for @xmath0ph@xmath1 in its ground electronic state . 
 this line list , called salty , contains almost 16.8 billion transitions between 7.5 million energy levels and it is suitable for simulating spectra up to temperatures of 1500  k. it covers wavelengths longer than 1  @xmath2 m and includes all transitions to upper states with energies below @xmath3  @xmath4 and rotational excitation up to @xmath5 . 
 the line list is computed by variational solution of the schrdinger equation for the rotation - vibration motion employing the nuclear - motion program trove . 
 a previously reported _ ab initio _ 
 dipole moment surface is used as well as an updated ` spectroscopic ' potential energy surface ( pes ) , obtained by refining an existing _ ab initio _ surface through least - squares fitting to the experimentally derived energies . 
 detailed comparisons with other available sources of phosphine transitions confirms salty s accuracy and illustrates the incompleteness of previous experimental and theoretical compilations for temperatures above 300 k. atmospheric models are expected to severely underestimate the abundance of phosphine in disequilibrium environments , and it is predicted that phosphine will be detectable in the upper troposphere of many substellar objects . 
 this list is suitable for modelling atmospheres of many astrophysical environments , namely carbon stars , y dwarfs , t dwarfs , hot jupiters and solar system gas giant planets . 
 it is available in full as supplementary data to the article and at www.exomol.com . 
 molecular data ; opacity ; astronomical data bases : miscellaneous ; planets and satellites : atmospheres ; stars : low - mass ; stars : brown dwarfs . 
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