Question

the table below lists information for seven Cepheid variables where ‘Period’ is the pulsation period of the star, and ?/?⊙ is the luminosity in solar units.

Period (days)	L/L⨀
4.5	835
7.2	1418
15.0	3761
29.3	8176
51.6	16623
82.8	28220
172.5	75140

a) Plot the PL relation for these stars using the logarithms of the values in the table (that is, ???(?) vs ???(?/?⊙)) and extract the slope and y-intercept of the relation the data define

Answer 1

Let's write the given data in logarithmic values,where

• 'P' represents pulsation period of star in days
• 'L/L' represents luminosity in solar units

log(P)	log(L/L)
0.6532	2.9217
0.8573	3.1517
1.1761	3.5753
1.4668	3.9125
1.7126	4.2207
1.9180	4.4506
2.2368	4.8759

slope of the equation (m) = (4.8759-2.9217)/(2.2368-0.6532) = 1.234

So, the equation be of the form y=mx+c,c:y-intercept

Then the equation is : log(L/L) = mlog(P) + C

log(L/L) = 1.234*log(P) + C;

Substitute any data from above table to get y-intercept;

3.9125 = 1.234*1.4668+C;

C = 2.1025

Therefore, the y-intercept is the luminosity of the star at start(i.e., log(P)=0 P=1).So, on the first day of period the luminosity = [(10)^2.1025] = 126.62 solar units.And the luminosity is increased by [(10)^1.234 = 17.14 solar units] for a period of one day(this relation is from the slope).