No-Detection Sources

Two sources (S76e, 20126+4104) had no detection. The reason was that we overestimated their flux and underestimated the integration time. Our estimation (Table. 2.6) shows that the integral line fluxes of S76e and 20126+4104 are 1393.3 and 235.2 Jy km/s with the line width 3.10 and 2.01 km/s separately. The channel width of YTLA is 7.05 km/s. YTLA averages the flux within the channel. If the line shape is sharp, YTLA will get a lower value by the averaging. Since our channel width is about 2 to 3 times wider than those in the literature, the integration time should be 4 to 9 times longer.

5.3 N

H

Abundance

Hoq et al. 2013 [9] found that N₂H⁺abundance increased due to the evolution of massive star-forming regions; it betrays the understanding of astrochemistry (Yu et al. 2019 [26]).

To solve the inconsistency, we expect that the N₂H⁺abundance decreases in the evolution with larger beam observing.

The abundance of specific molecular gas is the molecular column density divided by H₂column density. The eq. 5.2 shows the definition:

X_N2H⁺ = N_N2H⁺

N_H2 . (5.2)

To get the N₂H⁺ abundance (X_N2H⁺), we calculated the N₂H⁺ and H₂ column densities (N_N2H⁺ and N_H2).

We calculated the H₂column densities with the equation in Schuller et al. 2009 [20]:

N_H2 = Fν · R

B_ν(T_D)· Ω · κν · µ · mH

. (5.3)

where F_ν is the flux density, R is the gas-to-dust mass ratio, B_ν is the Planck function for a dust temperature T_D, Ω is the beam solid angle, κ_νis the dust absorption coefficient, µ is the mean molecular weight of the interstellar medium, and m_H is the mass of an hydrogen atom. We used the assumption in Gener et al. 2014 [7]: HMPO gas temperatures were

50 K, both HMCs and UCHii gas temperatures were 100 K, κ850µm = 1.42 cm²/g, and gas-to-dust mass ratio R = 100. Francesco et al. 2008 [6] used SCUBA to observe those sources in 850 µm. Table. 5.1 lists the fluxes observed by Francesco and the N_H2, which we derived.

Table 5.1: The H₂ column density. Column 2 is the flux observed in 850 µm by SCUBA [6].

Column 3 is the effective radius of the object (Francesco et al. 2008 [6]). Column 4 is the H2

column density, which was derived by the eq. 5.3

To calculate N_N2H⁺, we transferred the flux into intensity with the equation in Tielens et al. 2005 [22] first:

T = c²

2 ν² k Ω S. (5.4)

c is the light speed, ν is the line frequency in Hz, k is the Boltzmann constant, S is the flux, Ω is either the beam solid angle or the solid angle of the source, whichever is smaller. In our case, the sources were unresolved and we adopted the source size information from Francesco et al. 2008 [6] (in Table. 5.1).

The main component of N2H⁺ J=1-0 is F1F=23-12. The column density of N2H⁺ JF₁F=123-012 has the following relation (Mangum et al. 2017 [14]):

N_N2H+ = 1.20× 10¹²(T_ex+ 0.75) exp(^4.47_T

Texis the excitation temperature, Tbg = 2.7 K is the cosmic background radiation temper-ature, f is the fraction of the spatial resolution of the measurement filled by the source, J_ν(T) is defined as ^hν_k/(exp(^hν_kT)− 1), and the integral intensity is in K Km/s. Since we already considered the object size when we calculated intensity, f is 1. The integral in-tensity contains several components in N₂H⁺ J=1-0. Daniel et. al 2006 [3] listed the line strengths of all components in N₂H⁺ J=1-0. The contribution of JF₁F=123-012 in J=1-0

is 25.8%. We used this factor to estimate the intensity of JF1F=123-012. Table. 5.2 lists the T_exand integral intensity. Table. 5.3 lists the N_N2H⁺ and X_N2H⁺.

Source Intensity Intensity(JF₁F=123-012) Intensity(others) T_ex

K km/s K km/s K

DR21 21.9^+8.1_−4.7 5.65^+2.08_−1.21 106.3^a 10^a NGC7538 10.5^+3.8_−2.1 2.71^+0.97_−0.55 18.65^b 26^b S140 16.0^+5.5_−3.1 4.13^+1.43_−0.79 48.2^a 10^a 05358+3543 18.0^+6.3_−3.6 4.65^+1.64_−0.93 76.32^c,d 43,18^c,e Table 5.2: The intensity and Tex of N2H⁺. Column 2 is the intensity observed by YTLA. We used our observations’ result and eq. 5.4 to derived the intensity. Column 3 is the estimated flux of N2H⁺ JF1F=123-012. Column 4 is the intensity from other literature. Column 5 is the exci-tation temperature Tex, which we used in eq. 5.5. (a)Pirogov et al. 2003 [17]. (b)Womack et al.

1992 [24]. (c)Fontani et al. 2015 [5]. (d)It contains mm1 and mm3 because our observation can not separate them. (e)They are for mm1 and mm3 separately.

Source N_N2H⁺ N_N2H⁺ (others) X_N2H⁺ X_N2H⁺ (others)

10¹²cm⁻² 10¹²cm⁻² 10⁻¹¹ 10⁻¹¹

DR21 29.4^+10.8_−6.3 122.0^a 18.1^+6.6_−3.9 129,102^a,b NGC7538 24.2^+8.6_−4.9 20^c 15.3^+5.5_−3.1 20^c

S140 21.5^+7.4_−4.1 55.4^a 18.4^+6.4_−3.5 70,35^a,b 05358+3543 <62.2^+21.9,d_−12.4 117.8^e <151.7^+53.4_−30.2 – 05358+3543 >32.1^+11.3,f_−6.4 66.0^g >78.4^+27.6_−15.6 –

Table 5.3:The column density and the abundance of N2H⁺. Column 2 and 3 are the N_N2H⁺ from this work and others. Column 4 and 5 are the X_N2H⁺ from this work and others. (a)Pirogov et al. 2003 [17]. (b)Two values are from the different position. (c)Womack et al. 1992 [24]. (d)Our observation contains mm1 and mm3, and they can not be separated. This value is derived from the T_exof mm1. We consider it as a upper limit because mm1’s T_exis larger than the one of mm3.

(e)It is the column density of mm1 (Fontani et al. 2015 [5]). (f)It is derived from the T_exof mm3.

We consider it as the lower limit. (g)It is the column density of mm3 (Fontani et al. 2015 [5]).

The N₂H⁺column density and abundance of DR12, NGC7538, and S140 overlap each other, and they are HII region. 05358+3543 includes some early-stage objects, such as pro-tostellar and the starless core; its N₂H⁺abundance has an apparent increment. Figure. 5.1 is from the Hoq et al. 2003 [9]; it points out the abundance increases in the evolution.

Nevertheless, we have a contrast; the late-stage object has less N2H⁺abundance than the early-stage ones.

Furthermore, we compared our results with the evolution model of high-mass star-forming regions in Gerner et al. 2014 [7], including both the physical and chemical

mod-els. The blue line in Figure. 5.2 is their simulation result of N2H⁺abundance’s evolution.

They considered the object with r = 0.5pc. Four parts in Figure. 5.2 are IRDC, HMPO, HMO, and UCHii separately. The other lines are the results of this work. It shows the contrast trend in evolution. Thus, the result meets our original prediction: with a larger beam size, the late evolution stage’s high-mass star-forming region gets the less N₂H⁺ abundance.

Because our sources were unresolved, we used SUCBA’s object sizes to calculate their intensities and column densities. Potentially signal from a wider area was included in our observation. Therefore, we might overestimate the column densities depending on how much more signal was included. Our hypothesis states that N₂H⁺abundance in the surrounding area decreases with the evolutionary stage. The hypothesis then suggests that earlier stages would have a higher boost than the later stages.

The intensities of our observations are weaker than the ones of other literature. Thus, our calculations of the column density and abundance are also smaller. The ratio of our results to others varies in the physics quantity transformation. The different quantum models and assumptions of column density might cause the variance. Moreover, the in-tensity needs more observations to confirm because of the system uncertainty. Besides, four sources are not enough to confirm a trend. We have to observe more sources in the different evolution stages in the future.

Figure 5.1:N₂H⁺abundances separated by classification. The figure is from Hoq et al. 2013 [9].

With Mopra 22 m single-dish telescope, Hoq found that X_N2H⁺ increased as the high-mass star-forming evolution went on.

Figure 5.2: The comparison between the literature’s simulation and our observation. Gerner et al. 2014 [7] simulated the chemical evolution of high-mass star-forming regions in early stages.

They considered the object with r = 0.5pc. Four parts in the figure are IRDC, HMPO, HMO, and UCHii separately. The blue line is their simulation. The others are the results of this work. Our results show the contrast trend in evolution.

Chapter 6 Summary

Since YTLA started working in 2018, we chose two famous high-mass star formation regions (DR21, NGC7538) as the verification observation sources to test the N₂H⁺line observation. Then, we used S140, S76e, 05358+3543, 20126+4104 to investigate the variation of N₂H⁺abundance through the high-mass star-forming evolution.

By DR21’s observation, we found the telescope’s observing strategy caused the no-table pointing offset. The larger hour angle the source had, the larger offset it got. More-over, the pointing offset caused the flux loss. Pointing offset made the source close to the edge of the beam. The notable primary beam attenuation reduced the detected flux. We used a Gaussian model to fit the beam function and corrected the flux. The improvement of our correction for the flux loss was up to 27.1%. On the other hand, YTLA’s platform deformation by gravity caused the phase error in baselines. By comparing images reduced by visibility and amplitude data, we found the baselines’ phase error caused the flux loss of 15.3%. In addition to the pointing offset, it still had the unknown system uncertainty in the measurement. The uncertainty caused an extra 35.5% error.

S76E and 20126+4104 had no detection. Three Hii regions (DR12, NGC7538, and S140) have similar N₂H⁺ abundances. 05358+3543, a young object which includes the protostellar and starless core, has an apparent higher abundance than the others. The re-sult matches our prediction: observing with a larger-beam telescope, the high-mass star-forming regions’ early stages have higher N₂H⁺abundances. Nevertheless, with the sys-tem uncertainty and the lack of sources, we need more observations and sources to confirm

the trend in the future.

Appendix A