Credits: ESO

What is the Hertzsprung-Russell Diagram?

The Hertzsprung-Russell diagram, popularly known as the H-R diagram or CMD(colour-magnitude diagram), has shaped early astrophysics. The diagram evidences how the simple micro-phenomenon relating to the sub-atomic particles can influence the macro-phenomenon of whole galaxies and outer space.

The diagram was first plotted in the year 1911.It plots the luminosity of stars along the ordinate, and the colour of stars along the abscissa [1] and works to show the evolution of the stars and classify the stars which help to determine the further life cycle of the star(being supernovae or red-giant) The plot distinguishes the cluster of star points as:

  1. Main-Sequence Stars (Stars whose core Hydrogen fusion)
  2. Giants
  3. Super-Giants
  4. White Dwarfs

Which can be seen in this image (Credits:Chandra X-ray observatory)

For a deeper understanding of the concepts and analysis, please refer to information sources and other references. I came across an H-R diagram at the course of Rutgers University MOOC known as Analyzing the Universe.

In this project, we consider the data of Hipparcos stars which include many Hyades members facilitated by Penn State University’s Center of Astro-statistics.

Loading Data

options(warn = -1)
suppressPackageStartupMessages({
library(dplyr)
library(ggplot2)
library(plotly)
library(formattable)
})  
# Importing data from web;
Star<-read.csv(url("https://astrostatistics.psu.edu/datasets/HIP_star.dat"))
# Checking the original form of Data
formattable(head(Star))
HIP…..Vmag….RA………….DE…….Plx…..pmRA…..pmDE…e_Plx…B.V
2 9.27 0.003797 -19.498837 21.90 181.21 -0.93 3.10 0.999
38 8.65 0.111047 -79.061831 23.84 162.30 -62.40 0.78 0.778
47 10.78 0.135192 -56.835248 24.45 -44.21 -145.90 1.97 1.150
54 10.57 0.151656 17.968956 20.97 367.14 -19.49 1.71 1.030
74 9.93 0.221873 35.752722 24.22 157.73 -40.31 1.36 1.068
81 8.57 0.243864 -4.932115 23.43 -184.70 -172.67 1.28 0.642

The data format is weird, right ?

Preliminary indication from data and notes:

# Displaying cleaned data
Star1<-read.csv("Star_HR.csv")
Star1$LUMEN <- as.numeric(Star1$LUMEN)
Star1<- na.omit(Star1)
Star1$Vmag <- as.numeric(Star1$Vmag)

formattable(head(Star1))
Sr.no HIP Vmag RA DE PLX pmRA pmDE e_PLX BV LUMEN
1 2 9.27 0.003797 -19.498837 21.90 181.21 -0.93 3.10 0.999 3.049112
2 38 8.65 0.111047 -79.061831 23.84 162.30 -62.40 0.78 0.778 3.595387
3 47 10.78 0.135192 -56.835248 24.45 -44.21 -145.90 1.97 1.150 1.443442
4 54 10.57 0.151656 17.968956 20.97 367.14 -19.49 1.71 1.030 1.786803
5 74 9.93 0.221873 35.752722 24.22 157.73 -40.31 1.36 1.068 2.301652
6 81 8.57 0.243864 -4.932115 23.43 -184.70 -172.67 1.28 0.642 3.690455

So that now we have got our proper format of data, we can start with the rudimentary composition of data(i.e stars) and see what number of stars fall with which angle of the earth’s sky.

# About Data:
plx<-ggplot(Star1,aes(PLX))+geom_bar()+theme_minimal()
ggplotly(plx)

In the previous graph, we get a general idea about the distribution. Also, the graph lacks clarity. So now let’s consider the angle class (as we know the range) and classify data with respect to the observed parallactic angle of the star.

#Counting the no. of stars in perspective of distance:
d20_21<-Star1 %>% filter(PLX<=21) %>% count(PLX)
d20<-sum(d20_21$n)
d21_22<-Star1 %>% filter(PLX >21 & PLX<=22) %>% count(PLX)
d21<-sum(d21_22$n)
d22_23<-Star1 %>% filter(PLX >22 & PLX<=23) %>% count(PLX)
d22<-sum(d22_23$n)
d23_24<-Star1 %>% filter(PLX >23 & PLX<=24) %>% count(PLX)
d23<-sum(d23_24$n)
d24_25<-Star1 %>% filter(PLX >24 & PLX<=25) %>% count(PLX)
d24<-sum(d24_25$n)

parallax<-c("20-21","21-22","22-23","23-24","24-25")
quantity<-c(d20,d21,d22,d23,d24)
bar<-cbind(parallax,quantity)
bar<-as.data.frame(bar)
stat1<-ggplot(bar,aes(parallax,quantity))+geom_col(fill = "aquamarine4",color = "yellowgreen")+xlab("Parallactic angle")+ylab("Quantity of stars")+theme_minimal()
ggplotly(stat1)

Generating and Verifying H-R diagram:

Now that we know the distribution of parameters and other functions of data, we can easily plot the data satisfying the condition of H-R diagram.

t<-ggplot(Star1,aes(BV,Vmag))+geom_point(shape = 3)+theme_minimal()
ggplotly(t)
Wait a second ! This is not H-R Diagram, is it ?

Familiar H-R diagram:

In the above plot, we can clearly see the concentration of star for a trend and can deduce the analysis. But still it doesn’t look like our actual, famous and familiar H-R diagram. Why is that?

The answer to that in simple terms can be like: the absolute magnitude has not transformed with log condition (remember the occurrence a while back in Notes) We transform the “Vmag” by the formula of \((15 - Vmag - 5logPlx)/2.5\) (Bases to the 10) Why we do so? (Another important question) In practical terms, the range of values for stars is smaller in temperature than it is in luminosity. Most stars have temperatures between about 3000 K (M class stars) and 50,000 K (O stars). The range in luminosities is much larger—the faintest stars maybe 10,000 times fainter than the Sun, while the brightest stars maybe 10,000 times brighter than the Sun. In order to represent this wide range of values in one diagram, the Y-axis of a CMD or HR diagram is usually plotted on a logarithmic scale.[2]

gg<-ggplot(Star1,aes(BV,LUMEN))+geom_point(shape = 3)+theme_minimal()
ggplotly(gg)
# Inferring the H-R diagram in perspective of distance:
p<-ggplot(Star1,aes(BV,LUMEN,color = PLX))+geom_point(shape = 3,alpha = 0.5)+theme_minimal()
ggplotly(p)
# Tracing the fashion of graph:
p<-ggplot(Star1,aes(BV,LUMEN,color = PLX))+geom_point(shape = 3,alpha = 0.5)+theme_minimal()+geom_smooth(fill = "tomato",color ="yellow")
ggplotly(p)
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

References:

Documentation and Knowledge Base:

[1] https://astrostatistics.psu.edu/datasets/HIP_star.html