ohirstar-scaleheight-lifetime 1.0.0

Estimate a distribution and lifetime of star in the Galaxy.

ohirstar_scaleheight_lifetime

This ohirstar_scaleheight_lifetime module helps you estimate a plausible scale height and lifetime of stars.
The code was written during the investigation of the OH/IR stars distribution in the Galaxy (Uno et al. 2020). See the jupyternotebook (named as "OHIR-statistics.ipynb") for the detail of statistical analysis.

Requirements

The code was implemented on python3.7 and it uses the following python liblalies.

• numpy
• matplotlib
• scipy
• pylab

Setup

package installation

pip install git+https://github.com/yuriuno/ohirstar_scaleheight_lifetime.git

Data analysis

1. Scale height

1.1 Construct a simple Galactic disk model

import numpy as np
import matplotlib.pyplot as plt
from pylab import rcParams
from mpl_toolkits.mplot3d import Axes3D
from scipy import stats
import ohirstar_scaleheight_lifeitme.ohirstar_scaleheight_lifetme as sl

sh            = sl.ScaleHeight()
NUMBER        = 3990
SCALE_LENGTH  = 22   # kpc *exponential disk model
SCALE_HEIGHT  = 0.15 # kpc *gaussian (simplified sech z^2 disk model)
DIST_FUNC     = {'scale_length':SCALE_LENGTH, 'scale_height':SCALE_HEIGHT}
KINE_DIST     = 'near' # 'near' or  'far' * luminosity function based on near/far kinematic distance    
DETECTION_LIM = 0.122 # Jy   *SPLASH detection limit is 0.065 * 3 sigma 
mxyz, mlb, mflux = sh.model(DIST_FUNC, NUMBER, KINE_DIST)

1.2 Evaluate your model using K-S test

DATA   = np.load('./data/stat') # datatype: numpy strings
# DATA format: name, longitude, latitude, radial-velocity, expansion-velocity, velocity-uncertainity, flux-density, size, spot_num
REGION  = [{'l':[-28, -4], 'b':[-1.25, 1.25]},{'l':[4, 10], 'b':[-1.25,1.25]}, {'l':[14.35, 67.25], 'b':[-1.25,1.25]}] # specify the feild where you are evaluating
# dlb: np.array([l,b]) 
dlb     = np.array([[float(i) for i in DATA[1]],[float(i) for i in DATA[2]]])
p_value = sh.pvalue(dlb, mlb, mflux, DETECTION_LIM, REGION)
print(format(p_value,'.3f'))
>>> '0.531'

1.3 Quick visualization of the constructed model.

# 3D(X,Y,Z) [kpc]
sh.visualize(mxyz, mflux)

# 2D(l,b) [deg]
sh.visualize(mlb, mflux)

2. Lifetime

2.1 A most plausible lifetime

Lifetime of transient phenomenon such as the duration of OH masers associated with evolved stars
can be estimated by consideing the probability
of detecting m dissapeared maser sources in n samples in
a given amount of time; dT as demonstrated by Engels and Jimenes-Esteban (2007).

For example if you have m=3 maser sources vanished in n=100 samples after dT=10 years, you will get the most prausible lifetime ~300 years.

import numpy as np
from scipy.special import comb
import ohirstar_scaleheight_lifetime.ohirstar_scaleheight_lifetime as sl

M    = 30
N    = 445
DT   = 20
SPAN = 1000
lt   = sl.LifeTime(M,N,DT,SPAN)
lifetime = lt.lifetime()
print(format(lifetime,'.1f'))
>>> '296.7'

2.2 Upper limits of a lifetime

Meanwhile, the upper limit of OH maser lifetime with different significance levels can be estimated as follows

.

The upper limits for lifeitme of OH masers assuming at least m=3 maser sources vanish in
n=100 samples in dT=10 years will be 505, 1258, 2000 years depending on significance levels (1, 2, 3σ).

lifetime_upper_limit = lt.upper_limit()
print(lifetime_upper_limit)
>>> [326.90000000000435, 411.90000000000555, 512.900000000007] # 1 sigma, 2 sigma, 3 sigma

2.3 Quick visualization of the probability distribution

#  Pnm
xscale = 'linear'
type   = 'lifetime'
lt.visualize(xscale,type)

# Qnm
xscale = 'linear'
type   = 'upper_limit'
lt.visualize(xscale,type)