La sintaxis y la metafísica del lenguaje como metafísica del ser

The flux observed in th e visual from a disk accreting CV is potentially th e sum of th e lig h t from th e secondary star, th e prim ary (and th e boundary layer) an d th e accretion disk/bright spot. T aking each com ponent in tu rn , th e cool (Teff ~3000K ) la te type companion s ta r expected, an d som etim es detected in th e optical spectra of CVs (see section 2.3; W arner, 1995), ra d ia te s th e m ajor­ ity of its lig h t in th e in frared (e.g. P84). The w hite d w a rf which typically have tem p era tu re s of Teg ~ 1 0 -2 5 x l0 ^ K (Warner, 1996) can contribute flux in th e optical b u t they em it prim arily in th e u ltrav io let (P84). T his leaves th e accre­ tion disk.

For d w a rf novae in quiescence, th e accretion disks are found to have tem ­ p e ra tu re s typically Teg ~ lO^K a t th e in n er edge to ~5000K a t th e o u ter (e.g. VW Hyi; Wood e t al. 1986). However, although a larg e proportion of th e ac­ cretion disk is potentially cooler th a n th e w hite dwarf, th e em ittin g a re a of a n accretion disk is significantly larg e r th a n th e latter. T hus th e accretion disk is th e m ore lum inous component (since LocR^T^) an d dom inates th e lig h t in th e optical (as th e p eak of th e flux d istrib u tio n of th e accretion disk p eak s in th e optical). T his is especially th e case for th e nova-like sta rs w here th e

Chapter 2 54

m ass tra n sfe r ra te s in th e disk a re higher th a n for d w a rf novae in quiescence (Ldisk<xM(disk); e.g. W arner, 1996).

Therefore any fiiture reference to th e a p p a re n t or absolute V m ag n itu d e for d w a rf novae in quiescence essentially rep resen ts th e lum inosity of th e accre­ tion disk a t quiescence.

I calculated th e absolute m agnitudes in th e V ban d u sing th e sta n d a rd for­ m u la (e.g. Zombeck, 1990; W87)

My = TRy “H 5 — 5 log d ^ (2.4)

w here m^ is th e a p p a re n t visual m agnitude a t quiescence an d d is th e d is­ tance in parsecs. A is a factor, expressed in m agnitudes, which corrects th e absolute V m agnitude for th e effects of inclination, b rig h t spot, in te rste lla r reddening an d th e secondary (see section 2.4.1).

I estim ated th e u n certain ties on th e absolute V m agnitudes by u sin g th e distances derived by using th e u p p er an d lower lim its im posed on th e v alu es of Sk a s described previously.

2.4.1 T h e d is k lu m in o sity : E ffects o f in c lin a tio n , b r ig h t

sp o t, in te r s te lla r re d d e n in g a n d th e s e c o n d a ry

The orbital inclination of th e binary, th e presence of th e b rig h t spot (the region w here th e accretion stream im pacts on th e outer accretion disk), in te rste lla r reddening an d th e contribution of th e secondary s ta r can all p otentially affect

TUv an d therefore m u st in principle be ta k e n into account w hen determ in in g th e disk My.

Chapter 2 55

pie - AR Cnc, AY Psc, DV UM a and DO Leo which are high inclination system s w ith i>70°f an d T Leo, WW Cet, and DX And which a re low inclination sys­ tem s (see Table 2 . 1 an d 2.3 for references). O f th e rem ain in g system s, none

show any eclipses, suggesting th a t th e ir orbital inclinations a re not very high. W87 gives a n expression which corrects th e M v of a n optically thick disk for th e effects of inclination, tak in g account of limb d ark en in g (Paczynski & Schw arzenberg-C zem y 1980). This would suggest th a t th e sam e disk accret­ in g system viewed a t i=0^ is ~ 3.5 m agnitudes b rig h te r th a n w hen view ed a t

i=85°. R ecent accretion disk m odelling by Sm ak (1994) gives re su lts th a t agree w ith W87 for high m ass tra n sfe r ra te CVs (DNe above th e period gap an d NUs). However, for low m ass tra n sfe r ra te s (~10^’^gs~^ ; see HSC95) w hen th e disk is optically th in , Sm ak finds th a t M v is m uch less affected by th e b in ary incli­ n a tio n a n d th ere is no significant reduction in M v except w hen th e inclination is n e a r 90°. Since th e fain t d w a rf novae in my sam ple w ere likely observed a t m inim um , th e ir disks a re probably optically thin. Therefore th e effect of inclination on th e absolute V m agnitude resu lts is probably sm all.

The b rig h t spot, seen in photom etric lig h t curves as a b rig h tn ess “hum p”, is g enerally only prom inent a t high inclination (i>70°), an d in short period sys­ tem s w here th e im pact velocity of th e accretion stream on th e o u ter accretion disk is high (e.g. W87). Presum ably, however, th e b rig h t spot contributes flux in low -inclination system s spread over all orbital phases. F or m axim um u n i­ formity, I have used th e m ean V m agnitude, averaged over a n orbital cycle (but excluding eclipses) for all system s, irrespective of w h eth er they show a prom i­ n e n t orbital hum p. These m agnitudes should generally be considered a s u p p er limits to th e b rig h tn ess of th e “disk” proper. O f course, th e b rig h t spot lu m i­ nosity should properly be included in any estim ate of th e to tal accretion lu m i­

C hapter 2 56

nosity of a system .

For th e v a st m ajority of th e sam ple, th e effect of in te rste lla r absorption is unknow n an d w ithout specific reddening or extinction m easu rem en ts, only general assum ptions can be m ade about th e correction to be applied to th e in ­ dividual absolute m agnitudes. O f th e sta rs listed in Table 2.1, specific red d en ­ in g or extinction m easurem ents are available for only 2 high galactic la titu d e

CVs (T Leo, WW Cet) an d th e effect of in te rste lla r absorption w as found to be sm all in both cases (Ay=0,Ay =0.2 an d Eg_y <0.2 respectively; W87; H assall

1985).

W87 gives in te rste lla r extinction m easurem ents of a n u m b er of optically b rig h t (V<16) CVs m ostly a t lying a t low galactic latitu d e (b<|30|°) compiled firom th e lite ra tu re (cf. W87 Tables 1 an d 2). In th e v a st m ajority of cases, th e extinction is found to be less th a n Ay =0.3. In addition, colour excesses derived firom UV observations of a num ber of b rig h t d w a rf novae have also been found to b e sm all (H assall 1985).

I also used a n a ltern ativ e m ethod of estim atin g a n u p p er lim it to th e am ount of in te rste lla r absorption in th e line of sight to each of th e program m e sta rs u sin g a program (kindly m ade available by K. O. M ason) w hich estim ates th e H I colum n density to th e edge of th e G alaxy firom a lin e a r in terp o latio n of th e th re e H I m easu rem en ts (S tark et al. 1991) n e a re st to th e program m e star. I th e n used th e relationship betw een E(b-v) an d th e HI colum n density given in Zombeck (1990),

= 4.8 X 10^^ {a to m s cm~^ mag~^). (2.5)

Eb-v

In all cases, except for VY Aqr which w as found to have E b - v ^ 0 . 1 4 , E b _ v

C hapter 2 57

idence, th e effect of in te rste lla r absorption, in th e absence o f specific red d en ­ in g and/or extinction m easurem ents, on th e Mv(mm) re su lts is expected to be sm all.

O f th e sta rs in my sam ple, th e secondary s ta r h a s been detected in th e op­ tical sp ectra of th e long period system s DX And (Port=10 hours; D rew e t al. 1993) an d AR Cnc (Por6=5.15 hours; M ukai e t al. 1990) an d also in th e two sh o rt period system s BC UM a (Porf,=1.52 hours; M ukai e t al. 1990) an d DV U M a (Por6=2.07 hours; M ukai e t al. 1990). The secondary s ta r h a s also been detected in VZ A qr b u t no orbital period h a s y et been m easu red for th is sys­ tem . In th ese system s, th e secondary h a s been m easured to contribute less th a n ~5% of th e to tal V-band flux. A n um ber of th e other system s have opti­ cal sp ectra which show no evidence for secondary features, th u s th e contribu­ tio n of th e secondary to th e V b and lig h t is likely to be less in these. The effect of th e secondary s ta r on th e absolute V m agnitude resu lts is th u s likely to be minor.

W ith th e above argum ents in m ind I have, unless otherw ise stated , used A=0 th roughout th e analysis p resented in th is chapter.