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the well - determined fermi - lat spectra ( or upper limits , ul ) in the mev - gev band for several tev blazars are often used to derive stronger constraints on the diffuse extragalactic background light ( ebl ) , or to constrain the distance for bl lacs of uncertain redshift ( e.g. @xcite ) .
the underlying assumption of these studies is that the extrapolation of the fermi - lat spectrum to the vhe band is either a good estimate or an upper limit for the intrinsic vhe spectrum of the source , since they belong to the same hump in the spectral energy distribution ( sed ) .
the extrapolation is done either as a simple extension of the power - law ( or best fit ) model for the fermi - lat data , or using a one - zone synchrotron self - compton model ( ssc ) on the overall sed .
however , the observational evidence shows that this assumption is not well justified anymore .
blazars display a wide range in sed peak energies , as well as in emission components ( both in time and space along the jet ) .
the vhe band samples typically the highest energies of the emitting particle distribution , and is therefore more sensitive to even small changes in the acceleration and cooling processes .
observationally , irrespective of ebl absorption ( i.e. adopting the same ebl model for all sources ) , the band between he and vhe is the energy range where the spectrum of blazars typically changes the most , either because of the closeness of the sed peak or of the end of the emitting particles distribution .
therefore , the extrapolation to vhe of the he slope is in general never a good assumption .
this is particularly true for the high - energy - peaked bl lacs ( hbl ) which are bright in fermi and have been easily detected in the first years of operation @xcite .
these are characterized by the high - energy sed peak being very close to the lat band ( e.g. mkn421 , mkn501 , pks2155 - 304 , pks2005 - 489 , 1es1553 + 113 etc ) . for them ,
the he and vhe bands sample the two sides of the gamma - ray hump in the sed , and thus the intrinsic vhe spectra are much softer than the he spectra indeed this is the most common case among fermi - detected hbl @xcite .
the main question however is : can the vhe spectrum be harder than the he spectrum ? can thus the fermi - lat index be used as reasonable upper limit for the hardness of the vhe spectrum , or for its luminosity ?
concave he - vhe spectra have not been observed ( yet ) directly .
however , the observational ( as well as theoretical ) evidence is now showing this to be possible .
let us consider three facts .    1
.   bl lacs do show multiple spectral components in their synchrotron emission , which traces directly the shape of the electron distribution(s ) .
in several cases we have already seen the superposition of two different emission components at high electron energies , with a new component emerging over a previous / steadier sed .
classical examples are given by mkn 501 in 1997 @xcite , 1es1959 + 650 in 2002 @xcite and pks2155 - 304 in 2006 @xcite ( see e.g. fig .
the same can thus happen in the inverse compton emission .
the superposition of multiple spectral components is seen also outside specific flaring episodes , on long ( months to years ) timescales .
one of the most evident cases was given by pks2005 - 489 in the synchrotron emission ( fig .
[ f2 ] ) , during multi - wavelength campaigns in 2004 - 2005 .
the x - ray band in 2005 became more and more dominated by a new harder emission component emerging in the sed , which probably reached its maximum in june 2009 @xcite .
+   ( 5.08 or 3.93 @xmath2 @xmath3 ) .
even with the lowest galactic column density , in 2005 the x - ray spectrum can not be joined to the uv data from the optical monitor with a single smooth spectral component @xcite .
, width=283 ] 3 .   at vhe ,
intrinsic spectra as hard as @xmath4 are already observed , with a low ebl density ( even harder in case of higher ebl densities ) .
classic examples are given by 1es1101 - 232 @xcite , 1es0347 - 121 @xcite and especially 1es0229 + 200 ( fig .
[ f3 ] ) , which is characterized by such hard vhe spectrum up to @xmath510 tev @xcite .
this demonstrates that there exist physical conditions in blazars which can yield tev spectra as hard as @xmath6 , and with higher luminosity than in the synchrotron emission .
such conditions can in principle form also in specific zones of the jet , and/or in specific epochs .
the overall sed of such components can easily remain hidden below a more `` standard '' sed and emerge or become dominant only at vhe .
considering these three facts together , it becomes clear that spectra at vhe can very well be harder than at he .
this is true especially for those hbl where the fermi - lat index is closer to 2 than 1.5 ( or even steeper than 2 , as in ibl and lbl ) .
over such a wide range of energies ( 5 orders of magnitude ) , it seems not only possible but even likely that a combination of different spectral components either in time or from different particle populations or different emission mechanisms for the same particles can result in _ concave _ overall spectra .
it seems only a matter of time ( and statistics ) before up - turns somewhere in the overall 100 mev  10 tev band are directly and significantly detected in the simultaneous gamma - ray spectrum of some blazars .    it should not be surprising , because the observational ingredients are all there .
in fact , a possible example is already given by the fermi - lat spectrum of mkn501 @xcite , where a flaring episode has already produced a time - average he spectrum apparently hardening towards higher energies ( see fig .
[ f4 ] ) .
therefore , in general , fermi - lat spectra can not be reliably used as ul to a ) derive constraints on redshift , or b ) put stronger limits on the intensity of the ebl .
the results would be as weak / unreliable as their assumptions , and lead to gross over / under - estimates .
for ebl and resdhift studies , the @xmath6 limit for the intrinsic photon index is still a more robust benchmark than any fermi - lat extrapolation . although it is not a  hard " limit ( theoretically there are many mechanisms to obtain harder spectra , see e.g. @xcite ) , at present it still represents the borderline between reality and speculation ( for a full discussion , see e.g. @xcite ) .
observationally , intrinsic spectra with @xmath7 ( @xmath8 ) have never been observed so far in blazars at high electron energies ( e.g. @xmath9 ) , neither in the synchrotron emission nor in the inverse compton spectrum of low - redshift sources .
photon indexes of 1.2 - 1 are observed at x - ray energies in high - redshift , low - energy - peaked blazars ( typically fsrq ) , but these appear to be explained as low - energy cutoffs in the electron distribution , if not by internal absorption @xcite .
in fact , this is a spectral feature that could in principle appear in the fermi - lat band for some tev - peaked sources ( i.e. those where the lat band is deep in the valley between the two sed humps ) .
however , it would not automatically imply a similarly hard spectrum at vhe , because in such case the vhe band would correspond to the particle distribution well above the low - energy cutoff .    at present the ebl spectrum between 0.1 and 10 @xmath10 m
is constrained rather well ( mostly within @xmath550% ; @xcite ) , simply by using the range of spectra observed in blazars .
any further improvement beyond that requires a prediction of the blazars high - energy emission at a level of accuracy which seems not ( yet ) at hand @xcite .
the uncertainty is systematical , on which model and physical conditions are actually working in blazars . for a given he spectrum and overall sed ,
the range of possible vhe spectra is still large ( @xmath11 ) , even in a ssc scenario , depending on the choice of parameters , zones and adopted particle distributions ( see e.g. @xcite ) . and observations are demonstrating that we are still missing some fundamental aspects of the blazar physics .
one - zone ssc models can work _ a - posteriori _ , but can not be used reliably _ a - priori _ since blazars have multiple emission components , whose behaviour and interplay is still unknown
. a reliable prediction of the vhe spectrum from the he one is therefore not yet possible , at least in individual sources .    for a real progress in this field
, it seems now more useful and fruitful to fix the ebl to the most consistent and likely values ( e.g. @xcite ) , and to focus on improving our understanding of the blazar emission properties .
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fermi - lat spectra at high energies ( he , 0.1 - 100 gev ) are often extrapolated to very high energies ( vhe , @xmath0100 gev ) , and considered either a good estimate or an upper limit for the blazars intrinsic vhe spectrum . 
 this assumption seems not well justified , neither theoretically nor observationally . besides being often softer 
 , observations do indicate that spectra at vhe could be also harder than at he , even when adopting the limit of @xmath1 . 
 results based on such straightforward gev - tev extrapolations are in general not reliable , and should be considered with caution .