Physical parameters of Orion globule L 1616 and its illumination

[will-henney]

Roberto is investigating the parameters of the globule LDN 1616 in Orion.

We want to find the following parameters:

• [x] Distance from ionizing sources
• [x] Luminosity and spectral type of ionizing sources
• [x] Radius of globule
• [x] Density of globule
• [x] Ionizing flux incident on globule (units of photons per second per square cm)

[will-henney]

Relevant literature for finding ionizing luminosity from spectral class:

• Martins (2005)
• Smith (2006)

[will-henney]

[RobeReyes]

Piyali studied LDN 1616 and CB 28 close to eps Ori. On Table 1 ( Piyali ) they show some star that can photo-ionized LDN1616, we only considered HD 37468 and HD 37128 because their spectral type are 09.5V and B0Ia, respectively. We only considered this two sources because they have more temperature than the others.

Sigma Ori (HD 3746) has a luminosity nearly of $10^{4} L{o}$ and eps Ori (HD 37128) has a luminosity nearly of $10^{5} L{o}$ and they have a distance of 60($\pm$ 53) pc and 60($\pm$ 81) pc from LDN1616.

For ionizing flux incident to Sigma Ori we use the data from Table 4 on Martins and have $Q{0}=7.59\times 10^{47} s^{-1}$ and for eps Ori we estimated $Q{0}=6\times 10^{48} s^{-1}$, to obtain this values we need to extrapolated the data. Since $Q_{0}$ for Sigma Ori is an order lower than eps Ori, we can cosidered only eps Ori.

[will-henney]

Please check the values for the bolometric luminosities, which seem too low to me.

General comments: please give more details of how you obtain the values. For instance, in the case of the ionizing luminosity mention which tables were used from the Martins paper, and that we had to extrapolate to get the value for epsilon Ori because the table does not include B0.

[will-henney]

For the distance to the ionizing star, we will assume the average distance to the Orion OB stars of about 400 pc, with an uncertainty of about 20 pc. We cannot use the parallax for epsilon Ori because the uncertainty is too large.

For the distance to the globule, we will use the value of 384 +/- 5 pc, determined by Saha

@RobeReyes: please repeat the python calculations I showed you to find following:

• [ ] angular separation between star and globule
• [ ] physical separation on plane of sky between star and globule
• [ ] ionizing flux at the position of the globule

You will need to use the following python packages

from astropy.coordinates import SkyCoord
import numpy as np
import astropy.units as u

[will-henney]

For the globule radius, we will assume 0.1 degrees (estimated from the image)

@RobeReyes please also calculate the physical radius in cm and in parsec

[RobeReyes]

To estimate the distance, radius and ionizing flux we use the package astropy in python.

To the angular separation we use the data in astropy:

from astropy.coordinates import SkyCoord #import astropy and numpy
import numpy as np
import astropy.units as u

On table 1 in Piyali, the distance between epsilon Ori and LDN 1616 is the same that sigma Ori and LDN 1616 but the error is too big so we calculate taking the angular distance using the data in astropy

eps_ori = SkyCoord.from_name('eps ori')  #epsilon Ori coordinates
LDN_1616 = SkyCoord.from_name('LDN 1616')    #LDN 1616 coordinates
print('eps Ori coordinates:', eps_ori)
print('LDN 1616 coordinates:', LDN_1616)

separation = eps_ori.separation(LDN_1616)
print('the separation angular is:')
separation

and we have:

eps Ori coordinates: <SkyCoord (ICRS): (ra, dec) in deg
    (84.05338894, -1.20191914)>
LDN 1616 coordinates: <SkyCoord (ICRS): (ra, dec) in deg
    (76.75, -3.3517)> 
the separation angular is:
7∘36′26.1516′′

Now to calculate the distance between the stars and the globule, we suppose that the star and the globule are at the same distance from us, so we use geometry from a isosceles triangle and we have that the distance between the stars and the globules is $D=2d\sin(\theta/2)$, where $d$ is the distance to the Orion OB stars from us, we considered 400 (+/- 20) pc because in Piyali the error is big again and $\epsilon$ ori and $\sigma$ ori have the same distance to the globule, and $\theta$ is the angular distance.

from math import pi, e, sin, cos
import math
from IPython.display import display, Markdown
distance = 400*u.pc # distance to Orion OB stars
Distance = 2*distance*sin(math.radians((separation).value)/2)
Distance

note that we convert the angular distance to radians to compute the distance, so we have that the distance is

53.069723pc

For the ionizing flux $F=\frac{L}{4\pi d^{2}}$ we use the data from Table 4 in Martins for $Q_0$, we extrapolate the data because the spectral type of the stars are not in the table, and $d$ the distance that we compute

cms = (u.cm**2 *u.second)**(-1) # units for cgs
flux_io_sig_ori = ((7.59E47)/(1*u.second))/(4*pi*Distance**2) #ionizing flux for sigma ori
flux_io_eps_ori = ((6.0E48)/(1*u.second))/(4*pi*Distance**2) #ionizing flux for epsilon ori
flux_io_eps_ori_cms=(flux_io_eps_ori.to(cms)) #unit in cgs
flux_eps = format(flux_io_eps_ori_cms,'0.2E')  #to understand better
display(Markdown(rf'The ionizing flux of $'r'\epsilon$ Ori is 'f'{flux_eps}'))
flux_io_sig_ori_cms=(flux_io_sig_ori.to(cms)) #units in cgs
flux_sig = format(flux_io_sig_ori_cms,'0.2E')
display(Markdown(rf'The ionizing flux of $'r'\sigma$ Ori is 'f'{flux_sig}'))

and the results are

The ionizing flux of 𝜖 Ori is 1.78E+07 1 / (cm2 s)

The ionizing flux of 𝜎 Ori is 2.25E+06 1 / (cm2 s)

here we note that we can ignore the ionizing flux for $\sigma$ ori because it is an order less than $\epsilon$ ori.

Finally, for the globule radius, we can estimate that the angular radius is 0.2° (this is after looking $H_\alpha$ emission) and repeat the same idea that we use to compute the Distance between the star and the globule, so we have to convert the 0.2° to radians and use the distance in Piyali for the globule, 384(+/- 5) pc

angular_radius_LDN_1616 = 0.2*u.degree
distance_globule = 384*u.pc
globule_radius = distance_globule*sin(math.radians(angular_radius_LDN_1616.value))
print('The globule radius in pc is:',globule_radius)
print('The globule radius in cm is:',globule_radius.to('cm'))

and we have that the globule radius is

The globule radius in pc is: 1.3404101434459132 pc
The globule radius in cm is: 4.136073529634682e+18 cm

[will-henney]

I think that there may be a missing factor of 2 in the globule radius.