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the spectra of high - redshift quasars suggest that cosmic reionization was completed by @xmath9 @xcite , and recent measurements of the kinetic sunyaev - zeldovich effect constrain the duration of this process to @xmath10 @xcite . the galaxy population at @xmath1 may in principle be sufficient to reionize the universe ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but this hinges on the slope of the galaxy luminosity function at luminosities significantly below current detection thresholds , and on the fraction of hydrogen - ionizing photons that escape from galaxies into the intergalactic medium ( igm ) . the latter quantity , the lyman - continuum ( lyc ) escape fraction @xmath0 , can be directly measured at @xmath11 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? . observations of this type indicate an increase in the typical @xmath0 with redshift in the @xmath123 interval @xcite , and data - constrained models for galaxy - dominated reionization also require a redshift evolution in @xmath0 . simulations and theoretical arguments moreover suggest that @xmath0 may vary as a function of galaxy mass and star - formation activity .    at redshifts @xmath13 , measurements of the rest frame lyc flux ( at wavelengths @xmath14  ) are precluded by the opacity of the increasingly neutral igm . to probe @xmath0 throughout the reionization epoch , indirect measurements are instead required . some constraints on the _ typical _ @xmath0 in the reionization epoch may be obtained from fluctuations in the cosmic infrared background fluctuations @xcite , or by combining the observed galaxy luminosity function with ly@xmath15 forest data ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but it remains unclear whether and how @xmath0 may be assessed for individual galaxies at these redshifts .        here , we argue that since @xmath0 regulates the impact of nebular emission on the spectral energy distribution ( seds ) of galaxies , it should be possible to identify high-@xmath0 candidates from their rest - frame ultraviolet / optical seds at @xmath1 , at least for objects with very high escape fractions ( @xmath16 ) . @xcite , @xcite and @xcite have previously attempted to assess @xmath0 from photometric data , but spectroscopic signatures are likely to produce more reliable results for individual targets . recently , @xcite presented a spectroscopic method to place upper limits on the lyc escape fraction of high - redshift galaxies using metal absorption lines , but unlike their method , the one proposed here should be able to place both upper and lower limits on the escape fraction .    in sect . [ mechanisms ] , we describe the two main mechanisms capable of producing lyc leakage in galaxies and introduce the geometries adopted in our subsequent modelling of these . in sect . [ signatures ] , we present a simple spectral diagnostic that may be used to assess @xmath0 in the case of high - leakage objects , and discuss the role of metallicity , star formation history and dust attenuation on the relevant spectral features . focusing on the capabilities of the _ near infrared spectrograph ( nirspec ) _ on the upcoming _ james webb space telescope ( jwst ) _ , we derive the galaxy luminosity limits for the proposed method to estimate @xmath0 in sect .  [ discussion ] . a number of lingering problems with the proposed method are also discussed . [ summary ] summarizes our findings . all our calculations are based on a @xmath17 , @xmath18 , @xmath19 km s@xmath20 mpc@xmath20 cosmology , in rough agreement with the constraints set by the wmap 9-year data combined with @xmath21 measurments and baryon acoustic oscillations @xcite and the first planck results @xcite . whenever uv slopes and line equivalent widths are discussed , these quantities are given for rest - frame seds . there are basically two different mechanisms that can cause lyc leakage from star - forming regions  an radiation - bounded nebula with holes , and a density - bounded nebula ( also known as a truncated strmgren sphere ) . these two scenarios are schematically illustrated in fig . [ geometries ] , in which our model galaxy is depicted as a centrally concentrated ensemble of stars surrounded by a single hii region . the first case ( fig . [ geometries]a ) corresponds to the situation when supernovae or stellar winds have opened up low - density channels in the neutral interstellar medium ( ism ) through which lyc photons may escape without getting absorbed . the second case ( fig . [ geometries]b ) corresponds to a situation when the lyc flux from a very powerful star - formation episode `` exhausts '' all the hi before a complete strmgren sphere can form , thereby allowing lyc photons to escape into the igm . galaxies are admittedly more complex than the simple , toy - model geometries depicted in fig .  [ geometries ] and contain a spatially extended ensemble of hii regions with different sizes and densities . actual cases of lyc leakage are therefore likely to be due to mixtures of the two mechanisms . however , as we will demonstrate in sect . [ ew_beta ] , the spectral diagnostics we propose are very similar for these two limiting cases , as long as dust effects can be ignored . dust attenuation does , however , affect these two geometries differently , as discussed in sect . [ attenuation ] . the situation where lyc leakage is caused by high - velocity , lyc - emitting stars that venture far from the centres of galaxies is admittedly not well - represented by these simple geometries , but should effectively give rise to a situation similar to that in fig . [ geometries]b . the sed model results presented in this paper are based on the _ yggdrasil _ spectral synthesis code @xcite , which mixes single - age stellar population spectra to simulate arbitrary star formation histories . these are used as input to the photoionization code cloudy @xcite . the result is an age sequence of model seds which both stellar continuum emission , nebular continuum emission and nebular emission lines . in this paper , we adopt starburst99 stellar seds generated using padova - agb stellar evolutionary tracks at metallicities @xmath220.020 , assuming the @xcite universal stellar initial mass function ( imf ) throughout the mass range 0.1100 @xmath23 . since we are focusing on galaxies well into the reionization epoch , we limit the discussion to objects at @xmath24 , with ages @xmath25 ( roughly the age of the universe at @xmath26 ) . population iii galaxies ( at zero or near - zero metallicities ) may also exist at high redshifts and are predicted to exhibit pronouned lyc leakage @xcite . while such objects likely have too low masses to contribute substantially to the reionization of the universe , we briefly discuss models for such galaxies in sect . [ popiii ] , using stellar seds from @xcite . yggdrasil assumes that the nebular component of the overall galaxy sed can be treated as originating from a single , spherical and isotropic hii region ( as schematically depicted in fig . [ geometries ] ) with constant density and filling factor . in the case of radiation - bounded nebulae with holes ( fig . [ geometries]a ) , model seds with different @xmath0 are generated by varying the covering factor of the nebula in cloudy . in the case of density - bounded nebulae ( fig . [ geometries]b ) , different @xmath0 are instead achieved by truncating the nebula at a fixed fraction of the theoretical strmgren radius . in this paper , we adopt a constant hydrogen number density @xmath27 @xmath28 , a filling factor of 0.01 and a gas metallicity identical to that of the stars . however , the primary diagnostics that we discuss ( balmer recombination lines and nebular continuum in the rest - frame uv / optical ) are not sensitive to these parameter choices . we have moreover checked that our predictions for radiation - bounded nebulae with holes ( fig . [ geometries]a ) are in reasonable agreement with those of the @xcite model , which is based on a slightly different computational machinery . some of the ionizing photons produced by massive , hot stars are absorbed by the neutral hydrogen in the ism and produce prominent hii regions . as a result , photons at rest - frame wavelengths @xmath29  get reprocessed into emission lines and nebular continuum flux at longer wavelengths . a substantial fraction of the observed rest - frame uv / optical fluxes of young and/or star - forming galaxies is therefore expected to come from nebular emission rather than direct star light . since the relative contribution from nebular emission to the overall galaxy spectrum becomes smaller if some fraction of the ionizing photons escape directly into the igm , information about the lyc escape fraction is imprinted in the non - ionizing ( @xmath30  ) part of the sed . this is demonstrated in fig . [ spectra ] , where we present model seds for young starburst galaxies ( age 10 myr ) at metallicities @xmath31 ( fig . [ spectra]a ) and @xmath22 ( fig .  [ spectra]b ) . the line colours in each panel represent different @xmath0 ( 0.0 , 0.3 , 0.5 and 0.7 ) . at both metallicities , lower @xmath0 imply stronger emission lines and a more prominent balmer jump at 3646  . in fig . [ spectra]b , the entire slope of the uv continuum changes with @xmath0 , beacuse of the higher relative contribution from nebular emission at low metallicity . similar changes in the uv slope are seen at higher metallicities as well , albeit at younger starburst ages . the noticeable dependence of several spectral features on @xmath0 suggest that it should be possible to assess the lyc escape fraction from galaxy seds without actually measuring the lyc flux . the question is simply how to best retrieve the @xmath0 information from the rest - frame uv / optical sed that can actually be observed in the reionization epoch ( @xmath32  , since the flux at shorter wavelengths is absorbed by the neutral igm ) . the power - law slope @xmath2 ( @xmath33 ) of the uv continuum @xmath34 can in principle be used to gauge @xmath0 , since the addition of nebular emission to a young , purely stellar sed tends to shift the slope of the uv continuum in the redward direction and increase @xmath2 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the interpretation becomes ambiguous , however , unless a very blue uv slope is detected ( @xmath35 ) . the distribution of @xmath2 slopes among galaxies in the reionization epoch is still a matter of debate . @xcite reported an average @xmath36 for @xmath7 , but later studies have given no support for a typical slope this extreme and instead indicate @xmath37 . it is possible , however , that a subset of objects still display uv slopes substantially bluer than this ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the problem in inferring @xmath0 from @xmath2 is that @xmath2 also depends on age , metallicity and dust reddening . this is demonstrated in fig . [ uv_slope ] , where we plot the age dependence of @xmath2 for @xmath31 ( fig . [ uv_slope]a ) and @xmath22 ( fig .  [ uv_slope]b ) galaxies with either single - age stellar populations ( dashed lines ) or constant star formation rates ( solid lines ) . different line colours are used to indicate the impact of the lyc escape fraction in the case of an radiation - bounded nebula with holes ( fig . [ geometries]a ) . the arrow shows the shift in @xmath2 ( @xmath38 ) predicted for @xmath39 mag of @xmath40-band extinction of the stellar continuum ( corresponds to @xmath41 mag at a rest wavelength of 1500  ) in the case of @xmath42 , assuming the @xcite average large magellanic cloud ( lmc ) extinction curve . this amount of uv / optical extinction is consistent with several current estimates of the amount of dust affecting the uv slopes of @xmath24 galaxies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . at fixed @xmath39 mag , the @xcite attenuation curve gives a similar result ( @xmath38 ) . as seen in fig . [ uv_slope ] , the effect of @xmath0 on @xmath2 is very small for metal - rich galaxies ( fig . [ uv_slope]a ) but becomes substantial at low metallicities ( fig . [ uv_slope]b ) due to greater importance of nebular emission in the latter case . but even at metallicities as low as @xmath22 , it is only for extremely blue uv slopes ( @xmath43 ) that any sort of constraint on @xmath0 can be set from @xmath2 alone .    here , we use the original definition of @xmath2 given by @xcite , in which the uv slope is derived from the overall continuum flux ( stellar and nebular ) in 10 wavelength intervals ( chosen to avoid stellar and interstellar absorption features ) in the range @xmath442580  . the exact value of @xmath2 at any given age depends a bit on the exact wavelength region over which this slope is measured @xcite , but the overall trends seen in fig . [ uv_slope ] remain the same , regardless of the definition of @xmath2 used . it should be noted , however , that the 2175  dust feature can interfere with a few of the @xcite bands and make the uv slope behave in unexpected ways . in this paper , we therefore refrain from discussing attenuation recipies with very prominent 2175  bumps , like the average milky way extinction curve ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . we suggest that by combining the uv slope @xmath2 with the equivalent width ( ew ) of a balmer line such as h@xmath2 , it should be possible to identify galaxies with high escape fractions ( @xmath4 ) as long as the uv slope is @xmath45 after dust reddening corrections ( not far from the typical slope measured at @xmath1 , which is likely to be at least slightly affected by dust ; @xcite ) . this idea is demonstrated in fig . [ hb_beta_geom ] , where we plot the rest - frame ew(h@xmath2 ) against @xmath2 for @xmath31 for constant - sfr , dust - free models with different lyc escape fractions . results are shown for both geometries depicted in fig . [ geometries ] , i.e. an radiation - bounded nebula with holes ( solid lines ) and a density - bounded nebula ( dashed lines ) . the high - leakage models ( @xmath4 ; orange , green and blue lines ) are all shifted to the right in fig . [ hb_beta_geom ] ( i.e. towards lower ew(h@xmath2 ) ) compared to the no - leakage case ( red lines ) . since the model tracks remain separated up to the highest age considered ( 700 myr ; approximately the age of the universe at @xmath26 ) , this diagram suggests that @xmath0 can be assessed from a simultaneous measurement of ew(h@xmath2 ) and @xmath2 ( additional diagnostics can however improve the quality of this estimate , as discussed below ) . the results for radiation - bounded and the density - bounded models are next to identical at @xmath46 ( and , by definition , completely identical for @xmath42 ) . in the following , we will therefore focus on the radiation - bounded models .    at this metallicity ( @xmath31 ) , @xmath2 is seen to change very little as @xmath0 is increased , simply due to the fact that nebular emission has such a small impact on the uv slope ( fig . [ uv_slope ] ) . the equivalent width ew(h@xmath2 ) of course drops with increasing @xmath0 , but since nebular emission produces both the h@xmath2 emission line and part of the continuum below the line , the decrease is not as dramatic as one would expect if one assumed the underlying continuum to be purely stellar . similar diagnostic diagrams can in principle be formed for other balmer lines ( h@xmath15 , h@xmath47 , h@xmath48 etc . ) , but h@xmath2 seems to be a good compromise between observational limitations ( h@xmath15 redshifts out of the jwst / nirspec range already at @xmath49 ) and expected diagnostic value ( balmer lines beyond @xmath3 are weaker and have lower equivalent widths ) . other definitions of @xmath2 give rise to slightly different diagnostic diagrams , but the overall trends remain the same . while the [ oiii]@xmath505007 emission line can be measured over approximately the same redshift interval as h@xmath2 , and will in many cases be stronger , the equivalent width of this line is not as suitable as a diagnostic , since it is very sensitive to the ionization parameter of the gas . since metallicity is an important parameter in regulating the impact of nebular emission in galaxies @xcite , one expects diagnostic diagrams such as fig . [ hb_beta_geom ] to show some metallicity dependence . in fig . [ hb_beta_z ] , we display the same @xmath31 , constant - sfr model tracks for radiation - bounded nebulae as in fig . [ hb_beta_geom ] , alongside otherwise identical models at @xmath51 and @xmath22 . as expected , @xmath2 evolves more strongly with @xmath0 at low metallicities ( see fig . [ uv_slope ] ) , whereas ew(h@xmath2 ) displays a milder metallicity dependence . the latter effect is due to the greater contribution from nebular emission to _ both _ the h@xmath2 emission line and the underlying continuum at low metallicities . while a rough assessment of @xmath0 can be obtained even if the metallicity is unknown , a more precise estimate requires some handle on the metallicity . this is most readily obtained from the strengths of emission lines like [ neiii]@xmath503869 , [ oii]@xmath503727 and [ oiii]@xmath504959 , 5007 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , since data on these lines come `` for free '' when doing spectroscopy over the rest - frame wavelength interval ( @xmath525000  ) required to measure @xmath2 and ew(h@xmath2 ) . it should be noted , however , that many of the metallicity calibrations developed for these lines are based on the assumption of no lyc leakage , and may potentially give biased results if blindly applied to density - bounded nebulae with high @xmath0 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? as illustrated in fig . [ hb_beta_sfh ] , temporal variations of the star formation rate ( sfr ) can affect both ew(h@xmath2 ) and @xmath2 and need to be considered when attempting to assess the lyc escape fraction . galaxies with increasing star formation rates simply remain longer in the high ew(h@xmath2 ) , blue @xmath2 part of the ew(h@xmath2)-@xmath2 diagram , which makes the determination of @xmath0 easier than in the case of a constant sfr ( fig . [ hb_beta_geom ] ) . this is shown in fig . [ hb_beta_sfh]a , where @xmath31 models with exponentially increasing sfrs ( @xmath53 with @xmath54 yr ) at various @xmath0 are used . models with decreasing star formation rates are , however , more troublesome . in fig . [ hb_beta_sfh]b , we show the behaviour of models with exponentially declining star formation rates ( @xmath55 yr ) . these models evolve faster than the constant - sfr models of fig . [ hb_beta_geom ] and reach slightly redder @xmath2 at the highest ages considered . however , as there is no overlap between the different @xmath0 tracks , it should still be possible to estimate the lyc escape fraction . in fig . [ hb_beta_sfh]c , we consider a more extreme model with a very short burst ( @xmath56 yr ) of constant star formation , after which the sfr immediately drops to zero . since the lyman continuum flux decreases very quickly once star formation has ceased , models of this type evolve sharply to the right in the ew(h@xmath2)-@xmath2 diagram once the burst is over . during the post - burst phase , there is a brief period where model lines corresponding to different @xmath0 overlap , which means that an accurate assessment of @xmath0 would be very difficult in this part of the diagram . for these particular models , this happens at ages @xmath5715 myr ( @xmath58 ) , when the lyc flux has dropped to 215% of what it was right before star formation ceased . we stress , however , that galaxies will only rarely be caught in this brief transition phase . single - component models of the type used in fig . [ hb_beta_sfh]a  c are often assumed to be adequate in the interpretation of observational data on high - redshift galaxies , but real galaxies may well exhibit more complicated star formation histories , with several bursts with intermittent periods of low star formation in between . in fig .  [ hb_beta_sfh]d , we consider a sequence of equal - strength , @xmath56 yr long , constant - sfr bursts once every @xmath59 yr , with zero sfr in between . each burst shifts the models to slightly redder @xmath2 and lower ew(h@xmath2 ) , thereby causing a slight overlap between models with different @xmath0 .    in this context , the worst - case scenario would be to have a single young , low-@xmath0 burst superposed on an old , passively evolving population which contributes substantially to the h@xmath2 continuum ( thereby lowering ew(h@xmath2 ) ) while leaving the uv slope @xmath2 largely unaffected , since this could in principle mimic high @xmath0 in the ew(h@xmath2)-@xmath2 diagram . in fig . [ hb_beta_sfh2]a , we show the evolution of such a composite population , where a 1 myr old , @xmath42 model has been superposed on a 700 myr old , passively evolving population . as the mass ratio between the old population and the short burst is increased to @xmath60 , this @xmath42 model can wander into the region normally occupied by leaking galaxies with @xmath16 . if the mass ratio is increased to @xmath61 , the passively evolving population becomes completely dominant also in the uv , and shifts @xmath2 to very red values . however , the presence of an old , massive component gives rise to other tell - tale spectral signatures at the wavelengths probed by both nirspec ( 0.65 @xmath62 m ) and the mid - infrared instrument ( miri ; 527 @xmath62 m in imaging mode ) onboard the jwst . this is demonstrated in fig . [ hb_beta_sfh2]b , where we plot the seds of a 10 myr old , constant - sfr model with @xmath63 ( blue line ) and a 1 myr old @xmath42 model superposed on a passively evolving population with age 700 myr ( black line ) , where the old component is 300 times massive than the young population . both spectra have been redshifted to @xmath26 . these two models occupy a very similar position in the ew(h@xmath2)-@xmath2 diagram ( black triangle and orange @xmath56-yr age marker in fig . [ hb_beta_sfh2]a ) , but the continuum flux observed at @xmath64 m would be very different in the two cases ( much higher in the case of the two - component galaxy ) . the continuum flux at @xmath65 m comes for free when measuring @xmath2 and ew(h@xmath2 ) with jwst / nirspec , and jwst / miri can trace the continuum to even longer wavelengths . miri lacks the sensitivity to provide useful spectroscopic limits on the continuum , but miri imaging should yield competitive constraints . this is demonstrated in fig . [ hb_beta_sfh2]b , where we include the expected detection limits for jwst / nirspec low - resolution ( @xmath66 ) , 15 @xmath62 m spectroscopy ( red dashed line ) and compare these to the corresponding limits for jwt / miri imaging ( red triangles ) at @xmath6710 @xmath62 m . in both cases , we adopt an exposure time of 10h and require a @xmath68 detection .      in the quest to derive @xmath0 from the rest - frame uv / optical sed , dust attenuation is potentially a more serious problem than metallicity or star formation history , since this part of the sed may contain insufficient information to gauge the impact of lyc extinction . many recent studies of reionization - epoch galaxies suggest that these objects have suffered very little dust attenuation ( @xmath69 mag ; e.g. @xcite , but see for a different view ) . on the other hand , it does nt necessarily take much attenuation in the rest - frame optical or non - ionizing uv to have a considerable impact on the lyc  it depends on the spatial distribution of the dust compared to the gas and stars . predicting the effects of dust on galaxy seds is notoriously difficult , since the effective dust attenuation law depends not only on the amount and composition of dust , but also on the spatial distribution of stars dust and gas . in fig . [ dust_geometry ] , we schematically illustrate four different dust distributions ( two for each of the gas geometries of fig . [ geometries ] ) . this is not meant to be an exhaustive list of the possible dust distributions , but serves to illustrate a few different scenarios . in fig . [ dust_geometry]a and b , the dust is distributed in a uniform screen _ outside _ the hii region . in the cases depicted in fig . [ dust_geometry]a and c ( ioniziation - bounded nebulae with holes ) , dust has no direct impact on the leaking lyc flux , since the leakage is assumed to take place through holes that are devoid of both gas and dust . in the density - bounded nebula of fig . [ dust_geometry]b , on the other hand , the dust screen has a very pronounced effect on the escaping lyc . as an example of this , consider a dust screen giving a rest - frame @xmath40-band extinction of @xmath70 mag . extinction curves are notoriously uncertain in the far - uv , but if one adopts the average lmc attenuation curve presented by @xcite , this @xmath71 converts into a predicted lyc depletion factor of @xmath72 at 910   , but the @xcite milky way extinction curve  which extends to shorter wavelengths  predicts a similar lyc depletion factor ] . hence , the lyc escape fraction would effectively be limited to @xmath73 .    in the case of a foreground dust screen ( fig . [ dust_geometry]a and b ) , the rest - frame optical attenuation can straightforwardly be estimated from jwst / nirspec spectra of @xmath99 galaxies by measuring of the ratios of balmer emission - lines ( e.g. h@xmath2/h@xmath47 ) , since the intrinsic ratio can be estimated from recombination theory ( h@xmath2/h@xmath742.2 for a wide range of electron densities and temperatures , assuming case b recombination ) . however , if the dust is spatially mixed with the hii gas as in fig . [ dust_geometry]c and d , some fraction of the lyc photons will be absorbed by dust before they have a chance to ionize the gas ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and this will not be revealed by the balmer line ratios . while radiation pressure and dust sublimation act to produce a dust cavity around the ionizing stars , neither of these effects is sufficiently strong to prevent lyc photons from getting absorbed directly by dust in local hii regions @xcite . indeed , @xcite estimate that @xmath75 of the lyc photons produced in low - redshift starburst galaxies are typically absorbed by dust . since simulations of high - redshift galaxies suggest that when lyc escapes , it does so through essentially dust - free channels , we will limit the discussion to radiation - bounded nebulae with holes ( fig . [ dust_geometry]a and c ) . for both of these geometries , the effects of small amounts of optical attenuation ( @xmath70 mag ) on positions of galaxies in the ew(h@xmath2)-@xmath2 diagram are illustrated in fig ..  [ dust_corrections ] , assuming the @xcite average lmc attenuation law to capture the transport of radiation through dusty regions .    at low @xmath0 , a foreground dust screen ( attenuation vector represented by solid arrow ) has a pronounced effect on @xmath2 but almost no effect on ew(h@xmath2 ) , since the stellar continuum emerging through the screen still dominates the rest - frame uv , while the unattenuated continuum that escapes through the holes remains subdominant at wavelengths close to h@xmath2 . at high @xmath0 , the reverse is true : @xmath2 is largely unaffected by dust since the unattenuated stellar uv continuum escaping through the holes dominates over the dust - attenuated continuum , and ew(h@xmath2 ) is lowered due to the increasing importance of stellar h@xmath2 continuum emerging through the holes . hence , the attenuation vector changes direction and amplitude depending on where in the ew(h@xmath2)-@xmath2 diagram one started off .    if the dust is spatially mixed with the ionized gas ( fig . [ dust_geometry]c ) , the stellar non - ionizing continuum will still suffer @xmath70 mag of attenuation , but the balmer line ratios will reflect a value smaller than this , since part of the attenuation happened prior to photoionization . at fixed @xmath0 , the nebula will also appear fainter due to lyc extinction . here , we model this case by assuming that the star light entering the hii region is attenuated by @xmath76 mag before it has a chance to ionize the gas ( lowering the number of lyc photons that enter the gas by a factor of @xmath77 ) , and apply a further @xmath76 mag correction outside the hii region ( giving a total of @xmath70 mag , as before ) . other ratios of stellar to nebular attenuation can certainly be considered , but this serves to exemplify the ew(h@xmath2 ) and @xmath2 trends . the resulting lyc depletion factor is somewhat lower than suggested by @xcite and @xcite for local hii regions , but similar to that derived by @xcite for low - redshift starburst galaxies . our procedure gives rise to the dashed attenuation arrows in fig . [ dust_corrections ] . as in the case of the outer dust screen , the @xmath2 slope is reddened more at low @xmath0 than at high @xmath0 , but the overall reduction in nebular emission ( due to lyc extinction ) increases the relative impact of stellar h@xmath2 continuum on the emerging sed and decreases ew(h@xmath2 ) substantially at all @xmath0 .    at fixed @xmath78 , the two types of attenuation vectors discussed above have slightly different directions and amplitudes . moreover , a measurement of the h@xmath2/h@xmath47 balmer decrement will tend to underestimate the overall attenuation whenever lyc photons are lost due to dust extinction , as in the case where ionized gas and dust are mixed . for a given h@xmath2/h@xmath47 ratio , there will therefore be lingering uncertainties in how to correct the position in the ew(h@xmath2)-@xmath2 diagram unless the amount of lyc extinction can be assessed . for example , consider an object observed to lie close to the @xmath56 yr marker on the orange line ( @xmath63 ) in fig . [ dust_corrections ] . to correct the position of this object for dust effects , one needs to pick the right attenuation vector , and to move the object in the opposite direction in the diagram . if the balmer line ratios suggest @xmath70 mag , a correction assuming an outer dust screen would place the object on the green line ( implying @xmath79 ) , whereas a correction assuming mixed gas and dust would still place it on the orange line ( i.e. @xmath63 ) . these uncertainties are not easy to overcome from observations in the rest - frame uv / optical alone , but supporting observations in the rest - frame mid / far - ir could improve the situation ( as further discussed in sect . [ ir ] ) . the possibility that the effective attenuation law may have a more pronounced effect on emission lines than on the far - uv / optical continuum represents yet another complication . this phenomenon is observed in local starburst galaxies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and is most readily interpreted as due to temporal evolution in the opacity of star - forming regions  the youngest star clusters ( that contribute most of the lyc photons and the nebular emission ) tend to be more strongly affected by dust than the slightly older star clusters , which contribute substantially to the far - uv / optical stellar continuum ) . in principle , this effect could mimic lyc leakage in the ew(h@xmath2)-@xmath2 diagram by causing a substantial reduction in ew(h@xmath2 ) but only a modest reddening of @xmath2 . however , we find that the @xcite attenuation scheme  in which the nebular emission experiences a dust optical depth a factor of @xmath77 times than that of the stars  results in an attenuation vector no more extreme than those already included in fig .  [ dust_corrections ] . in order for a @xmath42 galaxy to be misclassified as an @xmath4 object , one requires both a higher ratio of nebular to stellar dust opacity  as in some of the more extreme objects discussed by @xcite  and substantial nebular attenuation ( @xmath80 mag , as revealed by e.g. the h@xmath81h@xmath47 emission line ratio ) . the radiation absorbed by dust is reradiated in the rest - frame mid / far - ir , and combined observations of the rest - frame uv / optical and mid / far - ir have been used to estimate the fraction of lyc photons absorbed by dust in local objects ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this dust emission lies out of range of the jwst for @xmath1 objects , but as further discussed in sect . [ detection_limits ] , observations with the atacama large millimeter / submillimeter array ( alma ) or the planned space infrared telescope for cosmology and astrophysics ( spica ) may be able to probe dust emission from galaxies at these redshifts . there are , however , many outstanding problems involved . for instance , the dust is heated by both the lyc , the non - ionizing uv and the resonant ly@xmath15 line . depending on the spatial distribution of gas , dust and stars and the overall velocity field , ly@xmath15 photons may escape from starburst galaxies at all redshifts , but for most galaxies in the reionization epoch , a substantial fraction of the ly@xmath15 photons that escape are scattered into huge and largely unobservable ly@xmath15 halos by the neutral igm ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , thereby causing potentially significant uncertainties in the ir radiation budget . the sed of dust emission also depends on the dust composition @xcite , which is highly uncertain even for low - redshift targets . the part of the sed required for the measurement of @xmath2 and ew(h@xmath2 ) falls within the wavelength range of the jwst / nirspec spectrograph for @xmath829 . the use of higher - order balmer lines instead of h@xmath2 ( h@xmath47 , h@xmath48 etc . ) would extend the range to @xmath83 , but at the expense of losing the [ oiii]@xmath505007 line , which is useful for getting a handle on the metallicity ( sect . [ metallicity ] ) . since the proposed method is applicable for relatively blue seds ( @xmath84 ) and positive ew(h@xmath2 ) , the most challenging aspect of these observations is to measure the @xmath3 continuum . using the jwst / nirspec exposure time calculator version p1.5 with the @xmath66 setting , we estimate that one should be able to get a @xmath85 measurement of the h@xmath2 continuum ( giving an error @xmath86 , since the error on the line flux will be negligible by comparison ) by integrating over @xmath87  bins in the rest - frame spectrum ) in 10 h for a 100 myr old , @xmath31 , @xmath63 , constant - sfr galaxy with stellar mass @xmath88 at @xmath26 . at @xmath89 , the corresponding mass limit would be @xmath90 . galaxies this massive are well within the detection limits of ultradeep hubble space telescope imaging , and many @xmath91@xmath92 objects have already been discovered in current @xmath24 samples . strong lensing by foreground galaxy clusters may boost the fluxes of high - redshift background objects by magnification factors of up to @xmath93100 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . by targeting lensed fields , it should therefore be possible to push these detection limits down to @xmath94 ( @xmath26 ) and @xmath95 ( @xmath89 ) , if @xmath93 is assumed . in terms of the rest - frame 1500 luminosities often used when measuring the luminosity function at high redshifts , this corresponds to @xmath6 at @xmath26 and @xmath8 at @xmath89 . these detection limits convert into star - formation rates of @xmath96 , placing them slightly above the level where stochastic sampling of the stellar initial mass function starts to have serious effects on the lyc flux of galaxies .    on a somewhat longer timescale , similar observations will also be possible with groundbased telescopes like the _ giant magellan telescope _ , the _ thirty meter telescope _ and the _ european extremely large telescope_.    as discussed in sect . [ attenuation ] , complementary observations of the rest - frame mid / far - ir with spica or alma could in principle provide information on the fraction of lyc photons destroyed directly by dust . such observations could also reveal the presence of heavily embedded components within the target galaxies . formally , the @xmath0 derived from jwst observations can only reflect the star formation that actually contributes to the rest - frame uv / optical sed , and extremely dust - obscured star formation ( undetectable in the optical , but bright at ir wavelengths , as in infrared - luminous galaxies at lower redshifts ; e.g. @xcite ) would shift this @xmath0 estimate away from that relevant for simulations of galaxy - driven reionization , where the _ total _ star formation rate of galaxies needs to be converted into a lyc flux emitted into the igm . based on the dust seds for star - forming dwarf galaxies presented by @xcite , we estimate that strongly lensed ( @xmath97 ) , @xmath99 galaxies with sfr @xmath98 yr@xmath20 should be detectable with alma in @xmath99 h exposures at @xmath100@xmath101 m . spica may be able to detect such lensed @xmath9 galaxies at @xmath102 m in less than 1 h , but this requires that one can push the photometry a factor @xmath67 below the formal spica confusion limit  for instance by using auxiliary , high - resolution data from other wavelength bands ( e.g. obtained with jwst or alma ) to subtract off the flux contribution from nearby interlopers .      in its current form , the proposed method can be used to assess @xmath0 for the brightest galaxies at @xmath1 , but is likely to provide interesting limits for galaxies exhibting very high lyc escape fractions only ( @xmath16 ) . however , the rest - frame uv / optical sed carries more information than contained in the ew(h@xmath2)-@xmath2 diagnostic , and stronger constraints can possibly be set by making use of the entire sed obtained from jwst / nirspec observations . in future papers , we intend to explore the true @xmath0 limits that can be obtained from spectroscopy using more detailed sed simulations . while it is likely that @xmath0 estimates for less extreme leakers may be obtained this way , the luminosity limits of the method are unlikely to change significantly . hence , only objects with @xmath6 ( stellar masses @xmath103 ) can be probed this way .    galaxies in this mass range may be insufficient to explain the ionization state of the universe at @xmath104 , and methods based on photometry rather than spectroscopy ( in the vein of @xcite , @xcite , @xcite ) will be necessary to estimate @xmath0 for objects at lower masses . while photometric methods are unlikely to provide strong constraints for individual targets , they can on the other hand be applied to larger samples of galaxies . in the future , we therefore also intend to investigate the likely @xmath0 limits that can be set using photometry with jwst / nircam and jwst / miri filters . population iii galaxies may exist at high redshifts and are predicted to have high @xmath0 @xcite . such objects may be detectable with jwst in strongly lensed fields @xcite and should be identifiable because of their unusual colours @xcite and spectra ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , at least for ages up to @xmath105 yr @xcite . while the low masses predicted for such galaxies ( total stellar mass perhaps no more than @xmath106 ; @xcite ) makes it unlikely that these objects would contribute substantially to the reionization of the universe , the spectral diagnostics we propose could in principle be used to assess @xmath0 for these galaxies as well . this is demonstrated in fig . [ popiii_fig ] , where we show the evolution predicted in the ew(h@xmath2)-@xmath2 diagram for a population iii galaxy experiencing a brief burst ( @xmath56 yr ) of zero - metallicity star formation , in the case of a radiation - bounded nebula with holes . the characteristic masses of population iii star formation is generically predicted to be top - heavy , but the exact stellar imf remains highly uncertain . here , we have used the @xcite stellar seds for a log - normal imf with characteristic mass @xmath107 , dispersion @xmath108 and wings extending from 1500 @xmath23 , but the results are similar for other imfs explored by @xcite during the early phase @xmath105 yr when population iii galaxies should be uniquely identifiable . at low ages , the strong impact of nebular emission on the uv slope at these low metallicities makes the model tracks curve upward in the ew(h@xmath2)-@xmath2 , but the tracks corresponding to different lyc escape fractions still remain clearly separated , thereby allowing an estimate of @xmath0 . at higher ages ( @xmath109 yr ) , ew(h@xmath2 ) drops while @xmath2 evolves very little , which causes substantial degeneracies between @xmath0 and the imf ( not shown , to avoid cluttering ) . one of the most important problems in observational cosmology is identifying the sources that reionized the universe . it is generally assumed that a substantial fraction of the ionizing photons were produced by galaxies , but other objects such as quasars ( e.g. * ? ? ? * ) , mini - quasars ( e.g. * ? ? ? * ) , micro - quasars ( e.g. * ? ? ? * ) and population iii stars ( e.g. * ? ? ? * ) may also have played a role . currently , there exist mostly indirect constraints on the timing of the reionization epoch . the spectra of high - redshifts quasars suggest that reionization was completed by @xmath9 @xcite , while observations of the cosmic microwave background can be used to put limits on the extent of the reionization period ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the detailed reionization history at @xmath110 remains highly uncertain , with statistics of ly@xmath15 emitters seemingly suggesting that the igm was still highly neutral at @xmath111@xmath112 ( e.g.  @xcite ) , while igm temperature measurements instead indicate that reionization was already mostly complete by these redshifts @xcite . the most promising prospect for constraining the reionization history in the near future is by observing the 21-cm line emission from the partly neutral igm . radio observatories such as lofar ( van haarlem et al . 2013 , subm . ) , mwa @xcite and paper @xcite are aiming for a detection at some point within the next few years . the 21-cm signal encodes a wealth of information about the physics of the reionization epoch , but the first generation of experiments will be focused on simple statistics such as the variance and power spectrum of the 21-cm brightness temperature . these statistics will not be able to constrain the evolution of the ionized fraction directly , but will have to be interpreted by comparing to simulations ( e.g. @xcite ) . most simulations to date include only galaxies as sources of ionizing photons , and use simplistic recipes to assign ionizing fluxes to the sources , tuned to reproduce the available observational constraints . with measurements of the lyc escape fraction in combination with observed uv luminosity functions , much of the `` wiggle room '' for these recipes would be eliminated . this in turn would make 21-cm measurements more powerful for constraining the sources of reionization by enabling better comparison between the 21-cm statistics predicted by different source models . if galaxies were responsible for the reionziation of the universe , significant lyc photon escape from these objects must have occurred at @xmath1 . our ability to put this scenario to the test is hampered by the neutral igm at these epochs , which precludes a direct measurement of the leaking lyc flux . however , since the lyc escape fraction @xmath0 regulates the relative impact of nebular emission on the seds of galaxies , indirect information on this parameter should be retrievable from the sed . as a first demonstration of this , we argue that extreme lyc leakers ( with @xmath16 ) may be identifiable from spectroscopic measurements of the equivalent width ew(h@xmath2 ) of the h@xmath2 emission line and the uv slope @xmath2 . by targeting strongly lensed galaxies , jwst / nirspec spectroscopy should allow this technique to be applied to galaxies with stellar masses @xmath103 and redshifts up to @xmath5 . we explore the impact of metallicity , star formation history and dust extinction on the ew(@xmath3 ) and @xmath2 diagnostics , and while all of these effects may complicate @xmath0 estimates to some extent , both the metallicity and the star formation history can be constrained by other spectral features that are readily detectable by jwst / nirspec . dust represents a more troublesome issue , since the rest - frame uv / optical sed accessible to jwst / nirspec at @xmath99 may contain insufficient information to properly gauge this effect . while several studies have indicated that lyman - break galaxies in the reionization epoch have suffered very little dust reddening , direct absorption of lyc photons by dust may still occur , with lingering uncertainties in the inferred lyc escape fraction as a result . heavily obscured star formation that contributes very little to the rest - frame uv / optical may in principle also bias @xmath0 estimates based on this part of the sed . we suggest that supplementary observations of lensed @xmath99 galaxies with alma or the planned spica mission may help constrain such scenarios by measuring the dust emission peak in the rest - frame mid / far - ir .    e.z acknowledges funding from the swedish national space board and the swedish research council . a.k.i . acknowledges funding from the ministry of education , culture , sports , science , and technology ( mext ) of japan ( kakenhi : 23684010 ) . the anonymous referee is acknowledged for helpful comments on the manuscript . ade , p.a.r . , et al . 2013 , arxiv1303.5076 alvarez , m. a. , finlator , k. , trenti , m. 2012 , apj , 759 , l38 benson , a. , venkatesan , a. , shull , j. m. 2013 , apj , 770 , 76 bergvall , n. , zackrisson , e. , andersson , b .- g . , arnberg , d. , masegosa , j. , stlin , g 2006 , a&a , 448 , 513 bergvall , n. , leitet , e. , zackrisson , e. , marquart , t. 2013 , a&a , in press ( arxiv1303.1576 ) bogosavljevi , m. 2010 , phd thesis , california institute of technology boutsia , k. , et al . 2011 , apj , 736 , 41 bouwens , r. j. et al . 2010 , apj , 708 , l69 bouwens , r. j. , et al . 2012a , apj , 752 , l5 bouwens , r. j. , et al . 2012b , apj , 754 , 83 calzetti d. , kinney a.l . , storchi - 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the fraction of ionizing photons ( @xmath0 ) that escape from @xmath1 galaxies is an important parameter when assessing the role of these objects in the reionization of the universe , but the opacity of the intergalactic medium precludes a direct measurement of @xmath0 for individual galaxies at these epochs . 
 we argue , that since @xmath0 regulates the impact of nebular emission on the spectra of galaxies , it should nonetheless be possible to indirectly probe @xmath0 well into the reionization epoch . as a first step , 
 we demonstrate that by combining measurements of the rest - frame uv slope @xmath2 with the equivalent width of the @xmath3 emission line , galaxies with very high lyman continuum escape fractions ( @xmath4 ) should be identifiable up to @xmath5 through spectroscopy with the upcoming james webb space telescope ( jwst ) . by targeting strongly lensed galaxies behind low - redshift galaxy clusters , jwst spectra of sufficiently good quality 
 can be obtained for @xmath6 galaxies at @xmath7 and for @xmath8 galaxies at @xmath5 . 
 dust - obscured star formation may complicate the analysis , but supporting observations with alma or the planned spica mission may provide useful constraints on the dust properties of these galaxies .