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despite their relative rarity , massive stars are dominantly dangerous for their environments .
this is a result of their mass and energy input via stellar winds and subsequent core - collapse supernovae ( sn ) . a overarching parameter for the life expectancy of a massive star concerns its strong mass outflow which is driven by radiative forces on millions of ionic spectral line transitions , providing it with its name `` line - driven wind '' .
on the one hand , mass loss is thought to be a key agent in revealing chemically processed material at the stellar surface , making it responsible for evolutionary scenarios such as the o @xmath0 luminous blue variable ( lbv ) @xmath0 wolf - rayet ( wr ) star @xmath0 sn sequence ( e.g. conti 1976 , chiosi & maeder 1986 , langer et al .
furthermore , it determines the stellar mass before collapse and is thus relevant for the type of compact remnant that is left behind ( i.e. neutron star or black hole ) . on the other hand ,
the role of mass loss may be equally relevant for the loss of angular momentum ( e.g. meynet & maeder 2003 ) .    with respect to the latter , it has been suggested that low metallicity ( actually low `` iron '' contents ; vink & de koter 2005 ) leads to less mass and angular momentum loss in low metallicity environments , perhaps resulting in a preference of long gamma - ray bursts ( grb ) in the early universe , but however interesting the metallicity dependence and the long grb puzzle may be , the temperature dependence of stellar winds and its role in the angular momentum evolution of massive stars has been highlighted more recently with respect to the possibility of _ bi - stability braking _ ( vink et al .
2010 ) .    given the crucial role that mass loss plays for massive star evolution , we discuss the theory of massive star mass loss and its implications , with a focus on the metallicity ( @xmath1 ) and effective temperature ( @xmath2 ) dependence .
we will see that the _ iron line opacity _ plays a dominant role in both cases .
the theory goes back to the early 1970s when lucy & solomon ( 1970 ) suggested that selective radiation pressure on spectral lines is capable of driving stellar winds from the surface of massive stars , proving an explanation for the p cygni profiles observed in the ultraviolet spectra of o - type stars in the late 1960s . for an extensive overview of both the theory and recent observational developments , such as wind clumping
, we refer the reader to puls et al .
the theoretical framework is based around the momentum equation :    @xmath3    where for simplicity the gas pressure has been ignored ( as the radiative pressure is the much more dominant factor in most parts of the stellar wind ) .
an oft - cited paper concerns the study of castor et al .
( 1975 , hereafter cak ) who expressed the radiative line acceleration @xmath4 as a function of the sobolev velocity gradient ( @xmath5 ) , involving a 2-parameter force multiplier ( @xmath6,@xmath7 ) parametrization .
subsequent improvements such as the inclusion of improved line lists by the munich group led to a reasonably good agreement with observed values ( e.g. pauldrach et al .
we note that the cak - type wind dynamics is based on the assumption that @xmath8 plays the same role as @xmath9 , such that the critical point of the wind is no longer the sonic point ( as in solar wind theory ) but further downstream .
the validity of this approach has been questioned by lucy ( 2007 ) .
furthermore , these works relied on the assumption that stellar photons could interact with the outflowing ions only once .    in order to account for multiple scatterings abbott & lucy ( 1985 ) developed a monte carlo methodology , which was updated and extended by vink et al .
( 2000 , 2001 ) . in these oft - used mass - loss prescription the velocity law
was originally adopted ( based on a semi - empirical motivation ) , but this assumption has recently been alleviated by mller & vink ( 2008 ) who express the line acceleration as a function of radius @xmath10 rather than the velocity gradient as done explicitly in cak theory .
the implication is also that the critical point is mathematically the sonic point .
the resulting mass - loss rates follow a scaling relation that only depends on the basic stellar parameters , approximately as :    @xmath11    over the entire range of @xmath12kk  except for the _ bi - stability _ jump around 25 kk , where the mass - loss properties are predicted to change drastically , with @xmath13 dropping by a factor of two ( pauldrach & puls 1990 ; vink et al . 1999 ) and the mass - loss rate jumping upwards by a factor of five ( vink et al . 1999
; see sect.[s : tdep ] ) .
massive stars rotate rapidly , with rotational velocities of up to 400 km / s .
this is understood to have dramatic consequences for their evolution and ultimate demise , which may involve the production of a long - duration gamma - ray burst ( long grb ) .    as a result of this rotation ,
the pole becomes hotter than the stellar equator ( von zeipel theorem ) , which enables a rather complex meridional circulation in the stellar interior . during this process
, nuclear processed material is transported from the core to the stellar envelope , thereby enriching the stellar surface with elements such as nitrogen ( n ) , which is produced during the cno cycle of hydrogen ( h ) burning .
later on , the combination of mass loss and rotation also leads to the transfer of products of helium ( he ) burning to the surface , enriching the atmosphere with carbon ( c ) during the final carbon - rich wolf - rayet ( wc ) phases before the stellar core is expected to collapse , producing a supernova ( sn )  in some cases in conjunction with a long grb .      the most popular explanation for the long grb phenomenon involves the collapsar model ( macfadyen & woosley 1999 ) in which a rapidly rotating core collapses and produces an accretion disk surrounding a black hole .
one of the persistent problems with the collapsar model was that the object not only requires a high rotational velocity at the very beginning of its life , but that it is required to maintain this rapid rotation until the end .
this is a significant challenge because strong stellar outflows are expected to remove angular momentum .
stellar models with rotation show that the objects not only remove up to 90% of their initial mass in winds when they have reached their final wolf - rayet phase , but as a result of this wind , the stars are also expected to come to a complete standstill .
the question is what is expected for wolf - rayet stars in low metallicity galaxies .
are they subject to similar mass and angular momentum loss ?
radiation hydrodynamic simulations show that stellar winds from massive o - type stars are driven by the radiation pressure on metal lines , and specifically on iron ( fe ) , despite the fact that it is such a rare element .
it should be noted that even in the metal `` rich '' environment of the milky way the h abundance is already 2500 times larger than that of fe .
however , owing to iron s highly complex atomic structure it has millions of line transitions , which makes it an extremely efficient absorber of radiation in the inner atmosphere around the sonic point , where the mass - loss rate is set ( vink et al . 1999 ,
puls et al . 2000 ) .
figure  [ fig : zrel ] shows the contribution of the different chemical elements ( h , he , cno , f ) to the total line acceleration for normal o - type stars . at solar @xmath1 ,
fe dominates the line acceleration near the sonic point , whilst its contribution drops significantly at lower density .
therefore , the fe line contribution is less important in the supersonic region where the wind terminal velocity is set ( panel b ) . and similarly at lower @xmath1 ( panels c and d ) . here
, the contribution of cno and elements such as cl , ar , p and s becomes highly relevant instead ( vink et al .
1999 , 2001 ) .
up to 2005 most stellar modellers assumed that due to the overwhelming presence of c in wc atmospheres , it would probably be c that drives wolf - rayet winds , rather than fe .
this assumption also implied that wc stars in low metallicity ( @xmath1 ) galaxies would have stellar winds equally strong as those in the galaxy , and still removing the required angular momentum .
it was for this reason that there was no satisfactory explanation for the long grb puzzle .
in 2005 , we performed a pilot study of wolf - rayet mass loss as a function of @xmath1 finding that although c may be the most abundant metallic element in wc atmospheres it is nonetheless the much more complex fe element that drives the stellar wind ( vink & de koter 2005 , grfener & hamann 2008 ) .
in other words , host galaxy metallicity plays a crucial role : objects that are born with fewer fe atoms lose less matter by the time they reach the end of their lives , despite their larger contents of cno material .
the striking implication is that objects in low metallicity environments  such as those characteristic for the early universe  can keep their angular momentum , enabling a potential grb event .
interestingly , there indeed appears to be a preference for long grbs towards lower @xmath1 systems ( e.g. vreeswijk et al .
as discussed at the end of sect .  [ s : theory ] , the mass - loss rates of massive objects are predicted to increase strongly when stars evolve towards the b supergiant regime . this @xmath14 jump is referred to as the bi - stability jump .
the mass - loss behaviour is depicted as the dotted line in fig .
[ fig : brott ] .
recent stellar models with rotation of brott et al .
( 2010 ) that include this vink et al .
mass - loss jump show a dramatic braking ( see solid line ) , which we refer to as _ bi - stability braking ( bsb)_. bsb might explain the general slow rotation of b supergiants . an alternative explanation for the slow rotation of b supergiants might involve a core he - burning nature for b supergiants ( see vink et al .
2010 for a detailed discussion ) .
the cause of the mass - loss bi - stability jump is that the most important line driving element fe recombines from fe iv to fe iii at 25 000 k and that suddenly the fe lines become much more effective as they fall in the wavelength range where the flux distribution is maximal .
the result is an increase in @xmath14 and a drop in terminal velocity .
the latter has been confirmed in observed data - sets ( e.g. lamers et al .
1995 ) , but the jump in mass - loss rate is still controversial ( e.g. crowther et al .
2006 , benaglia 2007 , markova & puls 2008 ) .
the relevance for stellar evolution is that when massive stars evolve to lower @xmath15  after the o star main sequence phase , they are expected to cross the bi - stability jump .
interestingly , lbvs brighter than log ( @xmath16 ) @xmath17 ( see fig .  [
fig : hrd ] ) . are expected to encounter it continuously - on timescales of their photometric variability , which we discuss in the next section .
22 000 k ( after humphreys & davidson 1994 ; smith et al .
2004 ; vink 2009).,width=340 ]    in the previous section , we discussed the physics of the bi - stability jump in the context of normal ob supergiants .
the jump might also play a role in the mass - loss behaviour of lbvs , in particular with reference to the normal `` s doradus '' type variations where the stars change their effective temperatures from values as high as 30 kk ( where they are identified as b supergiants ) to approximately 10 kk ( where they are identified as f supergiants ) . during these s dor excursions ,
the stars keep crossing the temperature range of the bi - stability jump ( see fig.[fig : hrd ] ) , thereby likely inducing variable mass loss .
such variable mass loss is in turn understood to be responsible for a non - uniform circumstellar medium , which could show up in the lightcurves and spectra of core - collapse sne  if lbvs were in an advanced enough evolutionary state .
current wisdom is that lbvs are not evolved enough ( e.g. langer et al .
1994 ) and that the lbv phase of evolution is the stage in which most of the outer hydrogen envelope is lost , prior to the objects turning to the much hotter wr phase . during this stage
, they are thought to be subject to core he - burning for another couple of 100 0000 years before they finally run our of fuel and collapse .
however , there have been recent observational hints that lbvs might explode early .
kotak & vink ( 2006 ) noted that the variable radio emission of some transitional core - collapse sne such as sne 2001ig and 2003bg might be the result of variable lbv progenitor mass loss , which was subsequently followed up with spectroscopic wind velocity variations in sn 2005gj ( trundle et al .
2008 ) . in the meantime ,
smith et al .
( 2007 ) have argued for lbv super - outburst circumstellar material being responsible for a number of luminous interacting sne , whilst gal - yam et al .
( 2007 ) identified an lbv - type hypergiant star in the pre - explosion image of sn 2005gl .
in other words , there appears to be a growing body of observational evidence that lbvs might explode already during their lbv phase of evolution .
it might turn out to be an interesting puzzle to reconcile these findings with the theory of stellar structure and evolution .
in this communication , we have presented a couple of examples of the type of information that mass - loss predictions can provide for our understanding of the evolution and fate of massive stars , especially with respect to sne and long grbs .
the manner in which these mass - loss predictions depend on the basic stellar parameters , such as @xmath1 and @xmath18 , can ultimately only be as good as the underlying atomic data .
extensive opacity data and linelists , such as those provided by kurucz & bell ( 1995 ) that have been used in our study , are thus of fundamental importance not only for the mass - loss predictions themselves , but also for understanding the lives and deaths of massive stars  over all cosmological epochs .
we present a brief overview of the theory of stellar winds with a strong emphasis on the radiation - driven outflows from massive stars . 
 the resulting implications for the evolution and fate of massive stars are also discussed . 
 furthermore , we relate the effects of mass loss to the angular momentum evolution , which is particularly relevant for the production of long and soft gamma - ray bursts . 
 mass - loss rates are not only a function of the metallicity , but are also found to depend on temperature , particularly in the region of the bi - stability jump at 21 000 kelvin . 
 we highlight the role of the bi - stability jump for luminous blue variable ( lbv ) stars , and discuss suggestions that lbvs might be direct progenitors of supernovae . 
 we emphasize that radiation - driven wind studies rely heavily on the input opacity data and linelists , and that these are thus of fundamental importance to both the mass - loss predictions themselves , as well as to our overall understanding of the lives and deaths of massive stars .