Question

16.1 The most easily observed white dwarf in the sky is in the constellation of Eridanus (the Ri Eridanus). Three stars make up the 40 Eridani system: 40 Eri A is a 4th-magnitude star simil to the Sun; 40 Eri B is a 10th-magnitude white dwarf; and 40 Eri C is an 11th-magnitude M5 star. This problem deals only with the latter two stars, which are s by 400 AUU eparated from 40 Eri (a) The period of the 40 Eri B and C system is 247.9 years. The system's measured trigono- metric parallax is 0.201" and the true angular extent of the semimajor axis of the reduced mass is 6.89". The ratio of the distances of 40 Eri B and C from the center of mass is aalac = 0.37. Find the mass of 40 Eri B and C in terms of the mass of the Sun, (b) The absolute bolometric magnitude of 40 Eri B is 9.6. Determine its luminosity in terms (c) The effective (d) Calculate the average density of 40 Eri B, and compare your result with the average density (e) Calculate the product of the mass and volume of both 40 Eri B and Sirius B. Is there a of the luminosity of the Sun. answer to the radii of the Sun, Earth, and Sirius B of Sirius B. Which is more dense, and why? departure temperature of 40 Eri B is 16,900 K. Calculate its radius, and compare your from the mass-volume relation? What might be the cause?

Please answer this question with clear procedure and explanation please! Thanks!

Answer 1

Please find the answer below, for direct answers go to the images where answers written with the blue pen, please give your feedback, and if not satisfied please comment. I will be glad if I can clear your doubts.

emc Distance to eri B and C ctystem ds guen elatiem dl pc () Here pods theャarallax angle Somimojsr amis og the reduced mass 3 Melaem C2) the reduced maas Su msg the masses tuo ustans un law Gip2 ove me and mc re the mas es op Eri B gravitatieral contant andトǐs the Ratio mc (4 m ae

Ratie Esi B te Janinesi he san velatiem Lc Here ie and e ave the duminesie ma and me ore the abiclute bie matric The above quton qes the Jwri Stegan Boltgmann equation or the and Te is eive tempuiature

b the xctio o its mass to veluroe (7) Hene Ve is its velume Velume e En b the Melatie dise this encp、Heaaiern un equuhm (7) (92 3 uoduct o mads and velume is given Ruo duct = mV 3

equactien () to bind d p c o,2 o1 4.48 pc eubtitute 89 go and 4.98 pc nel a = 6 89'' (4,98 pc ) Cenvent anc becondl to Hadian and au a. = 6.89", ( 1J1acl ) (4,98pc (3./X10-m) 20 62 65" 0. = 3.34 X lo-5n ad (15.44x16"m)

an 5 16 x lo'2m 661x l6" x 4 . ) Cewent ean unto decond uw above 1,34 x 1oK.. CA) ubiiliste 0.37 do aslac in e (41 me = 0.37 .(B) Ths ques me 031 me

1.3 098x1080 k n fern thuis vclue us iven as ballous 0,49 Mo 0.37 Use this equotion mcme1.34 loa 0 37 obove au, . equwuhon can be wi tten 2 x 10°。

whstibut yy or mo and 1.6 or mp in the cq (S) 리 o, o 114L。 16 W 0 05 Xlo6 =|q-3x101m

6.4 x 10 insuuen c) o8x for ms and 9.3 x lomo Ra in the equiation 9) URX (9.3x101), Snius B us aound us B us denser than Eri B becaus e at has Wanger masi and ushmalier

olius 3 SBius B: Substitute 2-1 x 1030kg vbgm and C1o) 3 the puupdict ma3s and vlume is uuch kuttene value Sur ins B is mu Jaser than that og bi

Reason for answer (d):

This is because the size of Eri B is lesser than the value calculate from the mass-volume relation. This makes Eri B to be very dense, becasue of which the electrons in it move with the relativistic speeds. This makes the electron degeneracy pressure in the Eri to be lesser than that calculated from non-relativistic approach.