Balmer temperature

Local thermal equilibrium (LTE) is an assumption that allows for the molecules to be in equilibrium with at least a limited region of space and remains an assumption when using the Boltzmann law for the relative populations of energy levels. The LTE assumption notwithstanding, observation of a series of transitions in the spectrum and measurement of their relative intensities allows the local temperature to be determined. We shall see an example of this in Section 4.4 where the Balmer temperature of a star is derived from the populations of different levels in the Balmer series. 

Substituting the value for the population ratio 2/ i = 5.15 x 1CT9 derived from the intensity of the transitions in the Balmer series into Equation 4.4 allows the Balmer temperature to be calculated ... 

Balmer temperature The temperature of a star determined by the presence of the B aimer series and hence the population of the n = 2 level in H atoms on the photosphere of the star. 

There are in principle an infinite number of series beginning at higher quantum numbers with i = 6, 7, 8, 9... but they become increasingly difficult to observe. For the higher n series to be seen in the spectrum the levels have to be populated, so some hydrogen atoms must be in the n = 5 level to see the Pfund series. We shall see that the presence of the Balmer series in the spectrum of a star is indicative of the stellar temperature, which is a direct consequence of the population of the energy levels. More of this in Chapter 4. 

The Balmer series is seen in many but not all stars because the first energy level in the series is an excited state with quantum number n = 2. There has to be a mechanism by which the excited stated is populated and this is the local temperature of the star. Hence only if the star is sufficiently hot will the spectrum contain the Balmer series. The strength of the Balmer series within the stellar spectrum can be used to derive a temperature for the surface of the star to compare with black body temperature and the B/V ratio. 

This is a similar value to the temperature of the Sun derived optically or from A.max in the black body spectrum. In a colder star the Balmer series is weaker still, but in a hotter star the Balmer series lines are stronger. In very hot stars the Balmer series may become weaker again due to collisional ionisation of H atoms, removing the electrons from the atoms completely. 

Observation of the Balmer series in the H atom implies population of the n = 2 level of the H atom and the temperature of the local environment... 

Determination of the temperature of the star from the intensity of the Balmer series and the population of n = 2 in the hydrogen atom... 

The compact initial state of the supernova ensured that the initial colour evolution is about five times faster than a normal Type IL At five to seven days the (B - V) colour evolution accelerated as line blanketing, initially from higher members of the Balmer series, but later from metal lines, mainly from the iron group, becomes important The climb towards maximum was accomplished at an almost constant temperature as measured by the (V - I) colour, but a further decline in temperature was seen in the post-maximum phase as the luminosity collapsed towards the radioactive tail. An increse in (U - B) occurred at 40 - 50 days, but this does not correspond to any change in photospheric temperature. This is presumably the result of a composition change working its way out to the photosphere. 

The optical spectra for the first 4 days while the supernova was rising to an initial local maximum were rather simple, showing broad Balmer lines. After two days (circa February 25), the spectrum showed He I A.5876 but no sign of Ca H and K or the IR triplet, due, presumably, to the high temperature that ionizes Ca II. After four days (circa... 

The velocities of the absorption minima of the Balmer lines are basically set by the density at a given velocity. The absorption minima are essentially independent of the luminosity of the model for reasonable values of the luminosity. At higher luminosity and temperature more hydrogen is ionized at lower radii and hence velocities, but more of the remaining hydrogen is excited, and these two effects are found to offset one another. Several aspects of the spectra do change significantly with the luminosity. One is the... 

Fig. 1. Doppler-free saturation spectrum of the hydrogen Balmer-a line compared to theoretical fine structure and Doppler profile at room temperature [4].

Fig. 3.3. Time traces for a JET discharge evolving from L-mode to Type I ELMy H-mode [15]. (NBI) is the input power into the plasma by fast neutral beams, Wtot is the total plasma energy (thermal + non-thermal component), Da (divertor) is the deuterium emission in the Balmer a line from neutrals coming into the plasma in the divertor area, average n is the average density of the discharge, Ti>core and Te,core are the ion and electron temperatures in the centre of the discharge and TelPed is the electron temperature at the top of the pedestal...

Simultaneously the intensity of the atomic Balmer lines (in this case D7) increases by nearly a factor of two. Thus, in the presence of molecules it obviously turns out that corrections to the estimated hydrogen flux may be required in such a form that the atomic S/XB (which is about 15 for densities 1018-1019 m 3 and temperatures above 15 eV) is replaced by an effective one, which is determined by the molecular deuterium flux rd-> ... 

Example Ionization Temperature from Spectral Data on the Series Limit. The ionization temperature of a hydrogen arc operating at 0.5 atm. is desired. An analysis of the spectrum shows that the last line discernible in the Balmer (Hydrogen) series has a quantum number of 5. According to the adjusted Inglis-Teller equation (L3)... 

Te can be derived using the ratio of the two lines [O III] A4363 and [O III] A5007, which have very different excitation potentials. Other line ratios can also be used as temperature indicators in nebulae, such as [N ii] A5755/6584 and [S III] A6312/9532. The Balmer and Paschen jumps, the radio continuum and radio recombination lines also allow to estimate the electron temperature, but the measurements are more difficult. 

A further problem is that the intrinsic hydrogen line ratios may deviate from case B theory. This occurs for example in nebulae with high electron temperature ( 20000 K), where collisional contribution to the emissivity of the lowest order Balmer lines may become significant. In that case, a line ratio corrected assuming case B for the hydrogen... 

From comparison of temperatures measured by different methods, this temperature fluctuation scheme led to conclude that temperature fluctuations are common in nebulae, with typical values of t2 = 0.03 - 0.05 (see references in Peimbert 1996, Stasinska 1998, Mathis et al. 1998, Esteban 2002). The case is not always easy to make the determination of the continuum in the vicinity of the Balmer jump is difficult, the combination of data from different instruments for the comparison of far infrared data with optical ones involves many potential sources of errors, lines of 0++ and of H are not emitted in coextensive zones etc. .. Nevertheless, the observational results seem overwhelming. And, as noted by Peimbert (2002), the value of t2 found in such a way is never negative ... 

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