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recent reviews on the presence of temperature variations in pne have been presented by esteban ( 2002 ) , liu ( 2003 , 2006 ) , and torres - peimbert & peimbert ( 2003 ) . of
the well observed pne about one third can be fitted reasonably well by 1d static chemically homogeneous photoionization models , but two thirds show temperature variations that are substantially larger than those predicted by simple photoionization models . in this paper
we review further evidence in favor of the presence of large temperature variations in pne .
we discuss possible causes for these variations and their effect on the determination of chemical abundances of pne .
we discuss the proper procedure to obtain accurate abundances for chemically homogeneous and for chemically inhomogeneous pne .
peimbert ( 1967 , 1971 ) found that the determinations of @xmath1([o  iii ] ) , the temperatures based on the @xmath2 ratio , are considerably larger than the determinations of @xmath1(balmer ) , the temperatures based on the intensity ratio of the balmer continuum to a balmer recombination line ; he interpreted this result as being due to the presence of temperature variations over the observed volume . to study this problem , peimbert defined the mean square temperature variation , @xmath0 ; typical simple photoionization models yield @xmath0 values in the 0.003 - 0.015 range .
peimbert and collaborators , also developed equations to derive the abundances for chemically homogeneous nebulae with @xmath3 ( peimbert 1967 ; peimbert & costero 1969 , ruiz et al .
2003 , peimbert et al .
the large differences between @xmath1([o  iii ] ) and @xmath1(balmer ) have been confirmed by several authors for a large number of pne ( e.g. liu & danziger 1993 ; zhang , liu , & wesson 2004 ) .
peimbert , storey , & torres - peimbert ( 1993 ) based on the computations by storey ( 1994 ) were the first to obtain larger o@xmath4/h@xmath5 values from oxygen recombination lines than from collisionally excited lines under the assumptions of @xmath0 = 0.000 and of chemical homogeneity .
most pne show this difference which has been usually called the abundance discrepancy factor defined by : adf(o@xmath4/h@xmath5 ) = ( o@xmath4/h@xmath5)@xmath6 / ( o@xmath4/h@xmath5)@xmath7 , ( e. g. liu 2006 , and references therein ) .
the adf(o@xmath4/h@xmath5 ) value is larger than predicted by simple photoionization models for about two thirds of the well observed pne .
a similar abundance difference for c@xmath4/h@xmath5 has been obtained by peimbert , torres - peimbert , & luridiana ( 1995a ) based manly on the line intensities compilation by rola & stasiska ( 1994 ) .
peimbert et al .
( 1995a ) compared the c@xmath4/h@xmath5 abundances derived from the c  ii @xmath8 4267 recombination line with those derived from the c@xmath4 @xmath9 1906 , 1909 collisionally excited lines . again
about one third of the adf(c@xmath4/h@xmath5 ) of the well observed pne might be explained by simple photoionization models but two thirds present values too large to be reproduced by these models .
zhang et al .
( 2005 ) have obtained large @xmath1([o  iii ] ) @xmath10 @xmath1(he  i ) differences for 48 pne that con not be explained by simple photoionization models . in section 4.2 we discuss their results .
torres - peimbert & peimbert ( 2003 ) presented seven mechanisms as possible sources of temperature variations , in what follows we will mention additional results in favor of some of these mechanisms .    _
deposition of mechanical energy : _ the central stars of pne inject mechanical energy into the expanding shells by means of stellar winds , bipolar flows , multipolar flows , and asymmetrical ejections , these processes produce shocks , turbulence , and an increase of the expansion velocity of the shell with time .
these processes are more important for some objects than for others and might be responsible for the spread in the observed @xmath0 values .
guerrero et al .
( 2005 ) and guerrero , chu , & gruendl ( 2006 ) found that the following pne are strong x - ray emitters : bd+30@xmath11  3639 , ngc  40 , ngc  2392 , ngc  3242 , ngc  6543 , ngc  7009 , and ngc  7027 , they also argue that this emission is due to shocks produced by fast winds or bipolar flows .
rowlands , houck , & herter ( 1994 ) derived @xmath1([ne v ] ) @xmath12 50,000 k for ngc  6302 and ngc  6537 , they also computed photoionization models and were not able to produce temperatures higher than 20,000  k and reached the conclusion that these temperatures were indicative of shock heating .
peimbert et al .
( 1995a ) found that the following pne with large velocity dispersions also show large temperature variations : ngc  2392 , ngc  2371 - 2 , ngc  2818 , ngc  6302 , and hu  1 - 2 , the last four are bipolar type  i pne .
medina , pea , & stasiska ( 2006 ) found , from a sample of 47 pne , that the velocity of expansion of the shell increases with age indicators , for example @xmath13 is larger for low density nebulae and it is also larger for nebulae with higher temperature stars .
furthermore by studing the line profiles medina et al .
( 2006 ) find that a substancial fraction of the material shows turbulent motions .
_ chemical inhomogeneities : _ see section 4.2 and the review by liu ( 2006 ) .
_ time dependent ionization : _ when a photoionization front passes through a nebula it heats the gas above the steady state value and some time is needed to reach thermal equilibrium . in the presence of localized density variations or a density gradient this process produces large temperature variations and might explain the presence of hot external halos in pne ( e.g. tylenda 2003 , sandin et al .
when the stellar ionizing flux decreases , or the density distribution along the line of sight changes , the outer regions of a nebula might become isolated from the stellar radiation field and will cool down before fully recombining , creating cold partially ionized outer regions , this might explain the low @xmath1(balmer ) values derived by luo & liu ( 2003 ) in the outer regions of ngc  7009 .
_ density variations : _ extreme density variations are present in most pne , as can be seen from optical images . for steady state photoionization models density variations
are not very important , but for time dependent processes the regions of higher density will reach equilibrium sooner than those of lower density .
_ deposition of magnetic energy : _ no specific models have been proposed yet for this mechanism .    _ dust heating : _ stasiska & szczerba ( 2001 ) have analyzed the effects of photoelectric heating by dust grains in photoionization models of pne .
this effect might be important in nebulae with large density variations .
this suggestion has not been tested yet for a specific model on any given pn .
_ shadowed regions : _ due to the presence of molecular globules inside ngc 7293 and ngc 6720 , two nearby pne , their presence is expected in many pne . according to huggins & frank ( 2006 ) , the covering factor of the globules in ngc 7293 amounts to about 5% .
the ionization of the gas shadowed by the globules will be produced by diffuse radiation , and consequently , the temperature of the shadowed gas will be a few thousand degrees lower than that of the material that is directly ionized by the central star ( mathis 1976 ) .
this mechanism alone might produce @xmath0 values around 0.01 in pne of the type of ngc 7293 and ngc 6720 .    to discriminate among the different possibilities ,
it is important to understand the signature of each process on the temperature and density distributions .
mechanical energy deposition , an increase in the local ionizing flux , and magnetic energy deposition will produce localized high - temperature regions relative to simple photoionization predictions ; while shadowed regions , the decrease of the local ionizing flux , and the presence of metal - rich inclusions will produce localized low - temperatures regions relative to simple photoionization predictions .
abundances correspond to those derived from recombination lines , if forbidden lines are used a @xmath0 different from 0.000 has to be adopted . in what follows we present evidence in favor of chemical homogeneity for most pne .    from chemical evolution models of the galaxy
it has been found that in the solar vicinity about half of the c enrichment of the ism is due to low and intermediate mass stars that end their lives as white dwarfs , and the rest is due to sn of type  ii ( e. g. carigi et al .
moreover according to other models most of the c enrichment is due to low and intermediate mass stars ( e. g. matteucci 2006 ) .
carigi ( 2003 ) has shown that the c / h values derived from c  ii recombination lines are in agreement with these models , while the c / h values derived from the 1906 and 1909 collisionally excited lines , under the assumption of @xmath1([o  iii ] ) and @xmath14 , imply lower c yields than those needed by the galactic chemical evolution models .
.stellar and nebular abundances for ngc 6543 [ cols="<,^,^,^,^",options="header " , ]     @xmath1([o  iii ] ) , @xmath1(he  i)@xmath15 peimbert et al.(1995b ) ; @xmath1(balmer ) zhang et al .
( 2004 ) ; @xmath1(he  i)@xmath16 zhang et al.(2005 ) ; a ) 3889,4471,7065 ; b ) 3889,4471,10830 ; c ) 6678,7281 ; d ) 4471,5876,6678 .
we consider that our knowledge on the density and temperature distributions and on the chemical composition of pne will increase considerably from the study of the four following problems .
the @xmath17(o  ii ) values derived from the o  ii lines of multiplet 1 , like those presented in table 3 , need to be determined again based on the atomic physics computations by bastin & storey ( 2006 ) .
objects with small he@xmath18 and he@xmath4 fractions and with most of their o in the o@xmath4 ionization stage will be particularly useful , those objects of this group with @xmath17(o  ii ) @xmath19(balmer ) will be chemically homogeneous , while those with @xmath17(o  ii ) @xmath20 @xmath17(balmer ) will be chemically inhomogeneous .
the idea that there are high density he@xmath5 regions embedded in low density h rich material might be tested by deriving @xmath1(he  i ) , @xmath17(he  i ) , and @xmath21(3889 ) based on accurate measurements of at least 10 different he  i lines in relatively low density pne without substantial he@xmath18 and he@xmath4 regions . those objects with @xmath17(he  i ) @xmath19(balmer ) will be chemically homogeneous , while those with @xmath17(he  i ) @xmath22(balmer ) will be chemically inhomogeneous .
there are at least seven possible mechanisms as sources of temperature variations . from the theoretical side , it is important to model the signature of each process on the temperature and density distributions . while , from the observational side , the combination of 3d kinematical models with high spectral resolution data , like those presented by barlow et al .
( 2006 ) , might permit to derive temperature and density distributions and consequently to single out the main mechanism responsible for the temperature variations in a given object .
finally accurate h , he , c , and o abundances of h - rich central stars , like those obtained by georgiev et al .
( 2006 ) for ngc  6543 , are needed to compare them with those nebular abundances derived from permitted and forbidden lines .
in this review we present a brief discussion on the observational evidence in favor of the presence of temperature variations , and conclude that many planetary nebulae show spatial temperature variations that are larger than those predicted by 1d static chemically homogeneous photoionization models . to determine accurate chemical abundances it is necessary to know the cause of these temperature variations and several possibilities are discussed . 
 the importance of this problem is paramount to test the models of stellar evolution of low and intermediate mass stars and of the chemical evolution of galaxies . 
 we conclude that the proper abundances for chemically homogeneous pne are those derived from recombination lines , while for the two - abundance nebular model the proper heavy element abundances relative to hydrogen are those derived from visual and uv collisionally excited lines adopting the @xmath0 values derived from @xmath1([o  iii ] ) and @xmath1(balmer ) .