Improved electromagnetic bias theory: Inclusion of hydrodynamic modulations

S O A U M 3 l I 0 | | 0 o s i : q d 3 i | j 8 u o | i ! S 3 i ) s ! : j B J S 3 A E A \ j . i o q s 3 i | j n i U O | J B I . I B A s o i | d L U I ' . I O A O A V O q L U O | ) l ! [ l i p O L U 0 1 u n : n X p o . i p , ù | a i y ^ • l l O ! ) l ? | l l p O l l l | ) 3 1 U . I 0 ) S | U O | | \ ! | . l l ' . A S ( l | | U O l | . ) ' | U l ! | S U O . > O C ] t i ] p o l U l l t i S l ! 0 . 1 1 ! S D ! ) S l 1 i : ) s O A B A \ J . I O I | S p o o | j | s : j | ; ) O A I ; A \ 3 U O ] X q p 3 s n i ? 3 X [ | B i j . i E d o . n : u o i p o s s s o . 1 3 . i n p u . i a q j n i S U O I J E U B / V Q ) u o i j B A a p 3 A B A \ S L I O ] a q j p u r : u o p n a s s s o . i a . m p i u a q j i i 3 3 A \ j 3 q u o p i ? | 3 . i . i o 3 p a z | | B I U . 1 0 U 0 L | ) S I S E K | | / \ | 3 . i a j 3 U U l | E 3 l [ J U O q m i p p U 0 U I I U 0 3 X { J s u o i p i u o i u | D i i u i u i À ' p o . i p A j j 0 } 3 I 1 Q S B | a 1 A 1 3 3 I H J O U O H U I L P Q • s £ [ Q c | 3 A I ; A \ S u o ] p i ù : j . i o q s q j o q . I O J s u o p d u o s a p p i a p s i j B j s U B I S S I I B Q U O U s p n p i n o j p a p u a j x o s i u i s q B i u . i o j s i q j ' X n B i i y ' L i o p E | m u . i o j | R 3 q X [ E i i B j u a i u 3 A U 0 3 ì ; s p i A O . i d o j u o i j d i u n s s E U B I S S I I U Q B . r a p i n i p a d o p A s p u a q j s ; ( i i Q d ) u o j j a u n j X j j s u a p X j q i q B q o . i d j u i o f Q g S u i p u o d s 3 . 1 . 1 0 3 a q j , • ( p a i u . i o j s u E . i j ) . i 3 q | ! H S E U A \ O U > [ o s [ f i ) s s . m j E . i p E i i b . I I 3 1 [ J S B | [ 3 A \ S B S 3 A B M S l I O [ J O S 3 d O | S p U B U 0 1 ) E A 3 | 3 3 l | J X q p 3 U U U . 1 3 . ) 3 p 3 . I E S J U S L l o d u i O O 3 S 0 l | A \ ' . I 0 J 3 3 A ( Q 9 ) ] B U 0 I S U 3 U I | p X I S B ¡ 0 U O i p i i n j S B p 3 S S 3 . l d X 3 3 . I B S J U 3 1 U 0 U I I E O I J S I J B J S 3 A B A \ ) . I 0 q S 3 l | J J O l I 0 1 J f i [ n p O l l [ ' . i a j j l ? 3 . 1 3 q p s d o | 3 A 3 p S y * S 3 A B A \ a a i ? j . m s j j o q s p i ù ; S u o | a s s q j i r a a A \ j 3 q s u o p s E . i a j u i a q j a q u o s a p U 3 l [ ] U B 3 3 3 U B [ B C ] U 0 I J 3 E 3 A B A \ J O 3 | d j 3 U | . l d 3 1 J J , • S ] l i a i I O C l l l l 0 3 3 A B A \ p 3 } B [ n p 0 l U . i a j . l O l [ S 3 1 ] ] U I O . I J £ ( S 3 A B A \ S l I O | „ S l I I A O U I J S B Ĵ p u c q M O . U B U a q j q s m S i n j s j p o j S J . I E C I O A V J O J U I p s p i A i p s q X E L U t t i n . [ } 3 3 C l s 3 A B M 3 3 E J . I I 1 S 3 l | ] J B l [ J a i U I l S S E 3 A \ ' | 3 p O l U U 0 I J 3 l i n j J 3 J S U B J J u o p E p i p o i u p . r e p i i E j s B S U I M O J J O J ' [ O O O Z ' " 1 ° > 3 f y l m l n 0 I ~ 1 3 Ì S 1 3 3 J J 3 p 3 3 n p a i i [ r j I U O . I J X | . i B 3 p J I q s i n S u p s i p o ] S B i q j A ] g 3 I l l l B l l X p 0 . i p X l | 3 l [ l 3 U L ) 3 p p i I B X j I J l i a p ] 3 A \ ' j S . t y ' p a . l S p i S U O O 3 . I B S U O | J E | n p O U I S I U l E l l X p O . i p X l ] U 3 l | A \ S B i q J A j g 3 l | J . I O J l ! O I J B | n i l I . I O J | E 3 ] Ì B U I 3 l [ } B U I | B U 0 1 J B . I B 3 p i A 0 . l d 0 ) S I [ B o S . 1 1 1 0 . I S C I B C I S U | J U J • . r e a i i q u o u . i o . r e s u i ] X s q j 3 q ' ( S 3 A B A \ 3 l I I J B [ n p O L l l ) S 3 A B A \ S U O ] 3 l I I À [ . I 3 p u n 3 l [ ] A q P 3 S I 1 E 3