Astrophysics PS15

Author

Will St. John + Caedan Miller + Elliott Lewis

Problem 1

  1. Using the recent formulation of the Cepheid period-luminosity relation from Riess et al. (2019), and the geometric distance to the Large Magellanic Cloud derived by Pietrzyński et al. (2019) (PDF of Nature article available on Moodle), re-cast the Cepheid Period-Luminosity relation in the Hubble Space Telescope’s F814W filter. It should take the form:

\[M_{F814W} = X \cdot (P/days) + Y\]

  1. What does this recasting imply the absolute magnitude should be for a Cepheid with a period of 1.1 days?

  2. Predict the apparent magnitude of the HST F814W filter of a Cepheid variable in the Local Volume galaxy Leo P with the same oscillation period. Use the distance to Leo P determined by McQuinn et al. (2015).

You may assume reddening-free situations for the Cepheids, and neglect the Wesenheit indices.

Answer: Given the magnitude

import numpy as np
import astropy.units as u

# b)
Y = 16.854 - 5 * np.log10(49.59E3) + 5
X = -2.96
P = 1.1
M = X * P + Y
print(M)

# c)
m = 5 * np.log10(1.62E6) - 5 + M
print(m)
-4.878970541455551
21.168604531257603

Problem 2

The Zwicky Transient Facility (ZTF) has revolutionized our understanding of pulsating stars. It has now discovered the majority of known pulsators of multiple classes. The manuscript by Chen et al. (2020) presents the ZTF catalog of pulsating stars. Read the manuscript to learn about the many types of pulsating stars.

  1. Using Table 2 of Chen et al. (2020), create a plot of pulsation period (in units of days) versus r-band magnitude for five different types of pulsating stars: Cepheid I, Cepheid II, RR Lyrae ab, RR Lyrae c, and Delta Scuti. Colorize and label each type of star in your plot. Use a logarithmic x-axis, with limits of 0.025 to 80 days. Use a linear axis for the magnitude, from +22 to +11.

If you’d rather start from presorted data, text files with the Table 2 data are provided for each pulsating star type are provided on Moodle.

  1. Comment on the differences between these pulsating stars, and what the expanded sample size provided by ZTF may help future research endeavors uncover or better understand.

Answer: If we measure the magnitude

from astropy.io import ascii
import matplotlib.pyplot as plt
data = ascii.read("https://content.cld.iop.org/journals/0067-0049/249/1/18/revision1/apjsab9caet2_mrt.txt")

cepI = data.group_by("Type").groups[1]
cepII = data.group_by("Type").groups[2]
RRab = data.group_by("Type").groups[7]
RRc = data.group_by("Type").groups[8]
D = data.group_by("Type").groups[3]
# plot r-band mag vs period for all stars
# color and label by star type
# log x axis, limits 0.025 to 80 days, linear magnitude axis, from 22 to 11
plt.scatter(D["Per"], D["rmag"], label = "Delta Scuti", alpha = 0.5)
plt.scatter(cepI["Per"], cepI["rmag"], label = "Cep I", alpha = 0.5)
plt.scatter(cepII["Per"], cepII["rmag"], label = "Cep II", alpha = 0.5)
plt.scatter(RRab["Per"], RRab["rmag"], label = "RR ab", alpha = 0.5)
plt.scatter(RRc["Per"], RRc["rmag"], label = "RR c", alpha = 0.5)
plt.xlabel("Period (days)")
plt.ylabel("r magnitude")
plt.legend()
plt.xscale("log")
plt.xlim(0.025, 80)
plt.ylim(22, 11)