Replies: 20 comments
-
|
From: pc***@fu*** (Patricio Cubillos) Hi, I would isolate two cases here, one when the broadening is Doppler dominated and another when is Lorentz dominated. Once, one is clear with each case, everything in between should be all right. Doppler is much simpler to test, just go to very low pressures (e.g., 1e-5 bar), there the line profile depends only in T, wn0, and the mass. For your test line, I get a Doppler HWHM = 0.014 cm-1 from Transit, which is consistent with the references you give. So, this part seems to be all right to me (I put my scripts in /home/patricio/ast/esp01/bart/transit/2017-04-27_voigt). Lorentz is more complicated. I have not found any source to confirm the formula, other than Goody (1995) and HITRAN. I have the impression that the HITRAN Lorentz broadening formula refers to air, as in Earth-like atmospheric air. Note that, unlike the equation in Goody (1995), the HITRAN equation does not depend on which is the gas mixture of the atmosphere. And after all, HITRAN was developed thinking on Earth-like atmospheres. I may well be wrong, it might be that all of the necessary info for the pressure broadening is contained in the pressures. But I don’t really know. Best,
|
Beta Was this translation helpful? Give feedback.
-
|
From: pc***@fu*** (Patricio Cubillos) By the way, there is a typo in Goody (1995), Equation 3.51 for the Lorentz width says n2, but it should read n*sigma2 (at least in the copy I saw). You can contrast this with the equation in this paper: p
-------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: mh***@kn*** (Michael Himes) I've been looking more into this and have discussed it with Joe to ensure I am understanding pressure/collisional broadening correctly. Most sources use some form of the rate of collision to determine the Lorentzian HWHM. This depends in part on the size of the molecules. The HITRAN formula does not consider that, so I am fairly certain that it will not be correct in situations with a high collision rate (i.e. Lorentz dominated). Is the collision rate used in transit to calculate the Lorentzian HWHM? If so, where is it calculated or what is referenced for the value? I did a calculation using the equation in the paper you linked; the result is a number far too large to be correct. I'm using cgs units (number density in cm-3, collision diameter in cm, k Boltzmann in erg K-1, temperature in K, mass in g). The number density I calculate is quite large; I am calculating that from the ideal gas law, N/V = P/(kT). As far as I know this should yield the correct number density, but that value is dominating the result so perhaps not. It's also possible that that equation only holds for lower temperatures and breaks do***@th***emperature I am using (1272 K). Also, regarding your Doppler test: For a Lorentzian test, I put the methane layer deeper in the atmosphere (pressure = ~3.35e-1 bars). This produces a line in transit with a FWHM of 0.19 cm-1. Using the HITRAN formula for the Lorentzian HWHM, I find a FWHM that is smaller than transit by a factor of 5. I'm pretty sure this is due to the HITRAN formula not considering the molecule's size which will affect the rate of collisions, as mentioned earlier. Best, From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> By the way, there is a typo in Goody (1995), Equation 3.51 for the Lorentz width says n2, but it should read n*sigma2 (at least in the copy I saw). You can contrast this with the equation in this paper: p On Apr 25, 2017, at 1:22 PM, Patricio Cubillos <pc***@fuailto:pc@fu***>> wrote: Hi, I would isolate two cases here, one when the broadening is Doppler dominated and another when is Lorentz dominated. Once, one is clear with each case, everything in between should be all right. Doppler is much simpler to test, just go to very low pressures (e.g., 1e-5 bar), there the line profile depends only in T, wn0, and the mass. For your test line, I get a Doppler HWHM = 0.014 cm-1 from Transit, which is consistent with the references you give. So, this part seems to be all right to me (I put my scripts in /home/patricio/ast/esp01/bart/transit/2017-04-27_voigt). Lorentz is more complicated. I have not found any source to confirm the formula, other than Goody (1995) and HITRAN. I have the impression that the HITRAN Lorentz broadening formula refers to air, as in Earth-like atmospheric air. Note that, unlike the equation in Goody (1995), the HITRAN equation does not depend on which is the gas mixture of the atmosphere. And after all, HITRAN was developed thinking on Earth-like atmospheres. I may well be wrong, it might be that all of the necessary info for the pressure broadening is contained in the pressures. But I don’t really know. Best, On Apr 24, 2017, at 9:43 PM, Michael Himes <mh***@knailto:mh@kn***>> wrote: Hi, I've been running more tests to try to match the width measured in transit, but I am unable to do so. I'll describe the two methods that have yielded the closest results. For both, I am working in cgs units, and FWHM values are in units of cm-1. In transit, the comparison line has FWHM of 0.0755 cm-1. (To get an accurate value, I lowered the wavenumber sampling interval to the minimum value before the code broke, which was at a value of 0.002). Since I am using a HITRAN line to compare transit to a pre-calculated Voigt function, I used the formulas provided by HITRAN. I assume these equations work properly or else someone would have complained to HITRAN by now. The formulas can be found here http://hitran.org/docs/definitions-and-units/ Using these formulas for alpha and gamma, the resulting Voigt profile has a FWHM of 0.02897 cm-1. I also used a more general equation that could be used for any line list. Those formulas are found in a number of places online; here are two that I referenced: I also referenced An Introduction to Modern Astrophysics by Carroll and Ostlie. In these, the formula given in wavelength space specifies that it is the FWHM, but the formula in frequency space it is not explicitly specified. I assume it is given as the FWHM as well, but in the event that it is not I have also included the resulting value assuming it is the HWHM. I noticed that the wavelength form has a factor of sqrt(ln 2) that the frequency form lacks, so I also tested it with this factor; the resulting FWHM values are a little smaller in this case as expected. Using those formulas, the resulting Voigt profile has a FWHM of 0.02586 cm-1; this is close agreement with the HITRAN method. If the Doppler width is instead given as the HWHM, then the resulting FWHM is 0.042 cm-1. I am more confident in the FWHM value of this method than the HITRAN method since it can be applied to any line list. Both methods are in disagreement with transit by a factor of***@le*** 1.8. I've checked over everything a few times and had a second set of eyes look over it to make sure I am not doing something obviously wrong. If you'd like to take a lo***@it***ourself, see Best, BART-devel mailing list -------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: jh***@ph*** (Joe Harrington) Some of the HITRAN values are for Earth air, which has a very different --jh-- X-Spam-Status: No, score=-1.9 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] I've been looking more into this and have discussed it with Joe to ensure I am understanding pressure/collisional broadening correctly. Most sources use some form of the rate of collision to determine the Lorentzian HWHM. This depends in part on the size of the molecules. The HITRAN formula does not consider that, so I am fairly certain that it will not be correct in situations with a high collision rate (i.e. Lorentz dominated). Is the collision rate used in transit to calculate the Lorentzian HWHM? If so, where is it calculated or what is referenced for the value? I did a calculation using the equation in the paper you linked; the result is a number far too large to be correct. I'm using cgs units (number density in cm-3, collision diameter in cm, k Boltzmann in erg K-1, temperature in K, mass in g). The number density I calculate is quite large; I am calculating that from the ideal gas law, N/V = P/(kT). As far as I know this should yield the correct number density, but that value is dominating the result so perhaps not. It's also possible that that equation only holds for lower temperatures and breaks do***@th***emperature I am using (1272 K). Also, regarding your Doppler test: For a Lorentzian test, I put the methane layer deeper in the atmosphere (pressure = ~3.35e-1 bars). This produces a line in transit with a FWHM of 0.19 cm-1. Using the HITRAN formula for the Lorentzian HWHM, I find a FWHM that is smaller than transit by a factor of 5. I'm pretty sure this is due to the HITRAN formula not considering the molecule's size which will affect the rate of collisions, as mentioned earlier. Best, From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> By the way, there is a typo in Goody (1995), Equation 3.51 for the Lorentz width says n2, but it should read n*sigma2 (at least in the copy I saw). You can contrast this with the equation in this paper: p On Apr 25, 2017, at 1:22 PM, Patricio Cubillos <pc***@fuailto:pc@fu***>> wrote: Hi, I would isolate two cases here, one when the broadening is Doppler dominated and another when is Lorentz dominated. Once, one is clear with each case, everything in between should be all right. Doppler is much simpler to test, just go to very low pressures (e.g., 1e-5 bar), there the line profile depends only in T, wn0, and the mass. For your test line, I get a Doppler HWHM = 0.014 cm-1 from Transit, which is consistent with the references you give. So, this part seems to be all right to me (I put my scripts in /home/patricio/ast/esp01/bart/transit/2017-04-27_voigt). Lorentz is more complicated. I have not found any source to confirm the formula, other than Goody (1995) and HITRAN. I have the impression that the HITRAN Lorentz broadening formula refers to air, as in Earth-like atmospheric air. Note that, unlike the equation in Goody (1995), the HITRAN equation does not depend on which is the gas mixture of the atmosphere. And after all, HITRAN was developed thinking on Earth-like atmospheres. I may well be wrong, it might be that all of the necessary info for the pressure broadening is contained in the pressures. But I don’t really know. Best, On Apr 24, 2017, at 9:43 PM, Michael Himes <mh***@knailto:mh@kn***>> wrote: Hi, I've been running more tests to try to match the width measured in transit, but I am unable to do so. I'll describe the two methods that have yielded the closest results. For both, I am working in cgs units, and FWHM values are in units of cm-1. In transit, the comparison line has FWHM of 0.0755 cm-1. (To get an accurate value, I lowered the wavenumber sampling interval to the minimum value before the code broke, which was at a value of 0.002). Since I am using a HITRAN line to compare transit to a pre-calculated Voigt function, I used the formulas provided by HITRAN. I assume these equations work properly or else someone would have complained to HITRAN by now. The formulas can be found here http://hitran.org/docs/definitions-and-units/ Using these formulas for alpha and gamma, the resulting Voigt profile has a FWHM of 0.02897 cm-1. I also used a more general equation that could be used for any line list. Those formulas are found in a number of places online; here are two that I referenced: I also referenced An Introduction to Modern Astrophysics by Carroll and Ostlie. In these, the formula given in wavelength space specifies that it is the FWHM, but the formula in frequency space it is not explicitly specified. I assume it is given as the FWHM as well, but in the event that it is not I have also included the resulting value assuming it is the HWHM. I noticed that the wavelength form has a factor of sqrt(ln 2) that the frequency form lacks, so I also tested it with this factor; the resulting FWHM values are a little smaller in this case as expected. Using those formulas, the resulting Voigt profile has a FWHM of 0.02586 cm-1; this is close agreement with the HITRAN method. If the Doppler width is instead given as the HWHM, then the resulting FWHM is 0.042 cm-1. I am more confident in the FWHM value of this method than the HITRAN method since it can be applied to any line list. Both methods are in disagreement with transit by a factor of***@le*** 1.8. I've checked over everything a few times and had a second set of eyes look over it to make sure I am not doing something obviously wrong. If you'd like to take a lo***@it***ourself, see Best, BART-devel mailing list [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list |
Beta Was this translation helpful? Give feedback.
-
|
From: pc***@fu*** (Patricio Cubillos) I believe that’s one reason. The HITRAN broadening parameters do not depend on the atmospheric composition, so I guess those gamma_air, n_air parameters refer to Earth-like air. There is another component too, the formula we are using in Transit requires the particle’s collision diameters, which are very uncertain for molecules. Sally and I were looking into that for a long time, but could hardly found well-documented values.
|
Beta Was this translation helpful? Give feedback.
-
|
From: mh***@kn*** (Michael Himes) I found a test of the Lorentz HWHM in transit/transit/test/lorentz.dat. It uses the collision cross sectional area and calculates a rate of collisions, so I think it should be more accurate than the HITRAN method. Based on the co***@th***nd of the file, it seems that this calculation matches the calculation in transit. Following that method, I calculate a Lorentz HWHM that is ~15% larger than that of the HITRAN method (for p=0.33516 bars, T = 1442.58 K). Based on the calculated alpha and gamma values, the profile should still be Doppler-dominated in the core of the line (alpha is ~1.7x larger). The width in transit is larger by a factor of ~ 5 indicating that gamma and/or alpha in transit is a larger value than what I am calculating. However, my calculated values are almost the exact same as those in transit's output. Transit prints out Lorentz: 8.76413e-03, Doppler: 1.48284e-02 (T=1442.58) My calculated values are Lorentz: 8.7654e-03, Doppler: 1.48322e-02 The slight discrepancy I attribute to using rounded values for constants rather than constants within a Python package such as Scipy. Also, I noticed two things that are a little weird with the line in transit further indicating that something is not quite right. The wings are cut off after a certain point, and the trough of the line is squared off with rounded edges. I had noticed this previously but I thought it was due to the large wavenumber sampling interval. However, the features are still there even with a small sampling interval (0.0005). If the trough is being chopped off as it appears then the wi***@ha***ax would be greater than actual, so this could be a source of the discrepancy. Michael From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> I believe that’s one reason. The HITRAN broadening parameters do not depend on the atmospheric composition, so I guess those gamma_air, n_air parameters refer to Earth-like air. There is another component too, the formula we are using in Transit requires the particle’s collision diameters, which are very uncertain for molecules. Sally and I were looking into that for a long time, but could hardly found well-documented values. On Apr 26, 2017, at 10:31 PM, Joe Harrington <jh***@phailto:jh@ph***>> wrote: Some of the HITRAN values are for Earth air, which has a very different --jh-- X-Spam-Status: No, score=-1.9 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] I've been looking more into this and have discussed it with Joe to ensure I am understanding pressure/collisional broadening correctly. Most sources use some form of the rate of collision to determine the Lorentzian HWHM. This depends in part on the size of the molecules. The HITRAN formula does not consider that, so I am fairly certain that it will not be correct in situations with a high collision rate (i.e. Lorentz dominated). Is the collision rate used in transit to calculate the Lorentzian HWHM? If so, where is it calculated or what is referenced for the value? I did a calculation using the equation in the paper you linked; the result is a number far too large to be correct. I'm using cgs units (number density in cm-3, collision diameter in cm, k Boltzmann in erg K-1, temperature in K, mass in g). The number density I calculate is quite large; I am calculating that from the ideal gas law, N/V = P/(kT). As far as I know this should yield the correct number density, but that value is dominating the result so perhaps not. It's also possible that that equation only holds for lower temperatures and breaks do***@th***emperature I am using (1272 K). Also, regarding your Doppler test: For a Lorentzian test, I put the methane layer deeper in the atmosphere (pressure = ~3.35e-1 bars). This produces a line in transit with a FWHM of 0.19 cm-1. Using the HITRAN formula for the Lorentzian HWHM, I find a FWHM that is smaller than transit by a factor of 5. I'm pretty sure this is due to the HITRAN formula not considering the molecule's size which will affect the rate of collisions, as mentioned earlier. Best, From: BART-devel <ba***@phailto:ba@ph***>> on behalf of Patricio Cubillos <pc***@fuailto:pc@fu***>> By the way, there is a typo in Goody (1995), Equation 3.51 for the Lorentz width says n2, but it should read n*sigma2 (at least in the copy I saw). You can contrast this with the equation in this paper: p On Apr 25, 2017, at 1:22 PM, Patricio Cubillos <pc***@fuailto:pc@fu***>mailto:pc***@fu***> wrote: Hi, I would isolate two cases here, one when the broadening is Doppler dominated and another when is Lorentz dominated. Once, one is clear with each case, everything in between should be all right. Doppler is much simpler to test, just go to very low pressures (e.g., 1e-5 bar), there the line profile depends only in T, wn0, and the mass. For your test line, I get a Doppler HWHM = 0.014 cm-1 from Transit, which is consistent with the references you give. So, this part seems to be all right to me (I put my scripts in /home/patricio/ast/esp01/bart/transit/2017-04-27_voigt). Lorentz is more complicated. I have not found any source to confirm the formula, other than Goody (1995) and HITRAN. I have the impression that the HITRAN Lorentz broadening formula refers to air, as in Earth-like atmospheric air. Note that, unlike the equation in Goody (1995), the HITRAN equation does not depend on which is the gas mixture of the atmosphere. And after all, HITRAN was developed thinking on Earth-like atmospheres. I may well be wrong, it might be that all of the necessary info for the pressure broadening is contained in the pressures. But I don’t really know. Best, On Apr 24, 2017, at 9:43 PM, Michael Himes <mh***@knailto:mh@kn***>mailto:mh***@kn***> wrote: Hi, I've been running more tests to try to match the width measured in transit, but I am unable to do so. I'll describe the two methods that have yielded the closest results. For both, I am working in cgs units, and FWHM values are in units of cm-1. In transit, the comparison line has FWHM of 0.0755 cm-1. (To get an accurate value, I lowered the wavenumber sampling interval to the minimum value before the code broke, which was at a value of 0.002). Since I am using a HITRAN line to compare transit to a pre-calculated Voigt function, I used the formulas provided by HITRAN. I assume these equations work properly or else someone would have complained to HITRAN by now. The formulas can be found here http://hitran.org/docs/definitions-and-units/ Using these formulas for alpha and gamma, the resulting Voigt profile has a FWHM of 0.02897 cm-1. I also used a more general equation that could be used for any line list. Those formulas are found in a number of places online; here are two that I referenced: I also referenced An Introduction to Modern Astrophysics by Carroll and Ostlie. In these, the formula given in wavelength space specifies that it is the FWHM, but the formula in frequency space it is not explicitly specified. I assume it is given as the FWHM as well, but in the event that it is not I have also included the resulting value assuming it is the HWHM. I noticed that the wavelength form has a factor of sqrt(ln 2) that the frequency form lacks, so I also tested it with this factor; the resulting FWHM values are a little smaller in this case as expected. Using those formulas, the resulting Voigt profile has a FWHM of 0.02586 cm-1; this is close agreement with the HITRAN method. If the Doppler width is instead given as the HWHM, then the resulting FWHM is 0.042 cm-1. I am more confident in the FWHM value of this method than the HITRAN method since it can be applied to any line list. Both methods are in disagreement with transit by a factor of***@le*** 1.8. I've checked over everything a few times and had a second set of eyes look over it to make sure I am not doing something obviously wrong. If you'd like to take a lo***@it***ourself, see Best, BART-devel mailing list [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list BART-devel mailing list -------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: rc***@kn*** (Ryan Challener) I don't know about the fl***@th***ottom of the trough, but the cutoff in the wings is, I believe, because we don't bother calculating the profile of each line across the whole spectrum. In theory, every line contributes across the entire spectral range, but in practice this contribution gets very small in the wings. We have to do this calculation tons of times (millions of spectral lines), so we can't afford to consider contributions far from the central peak or we'd be running transit for weeks. So we cut off after some threshold. Patricio, please correct me if I'm wrong. -Ryan From: BART-devel <ba***@ph***> on behalf of Michael Himes <mh***@kn***> I found a test of the Lorentz HWHM in transit/transit/test/lorentz.dat. It uses the collision cross sectional area and calculates a rate of collisions, so I think it should be more accurate than the HITRAN method. Based on the co***@th***nd of the file, it seems that this calculation matches the calculation in transit. Following that method, I calculate a Lorentz HWHM that is ~15% larger than that of the HITRAN method (for p=0.33516 bars, T = 1442.58 K). Based on the calculated alpha and gamma values, the profile should still be Doppler-dominated in the core of the line (alpha is ~1.7x larger). The width in transit is larger by a factor of ~ 5 indicating that gamma and/or alpha in transit is a larger value than what I am calculating. However, my calculated values are almost the exact same as those in transit's output. Transit prints out Lorentz: 8.76413e-03, Doppler: 1.48284e-02 (T=1442.58) My calculated values are Lorentz: 8.7654e-03, Doppler: 1.48322e-02 The slight discrepancy I attribute to using rounded values for constants rather than constants within a Python package such as Scipy. Also, I noticed two things that are a little weird with the line in transit further indicating that something is not quite right. The wings are cut off after a certain point, and the trough of the line is squared off with rounded edges. I had noticed this previously but I thought it was due to the large wavenumber sampling interval. However, the features are still there even with a small sampling interval (0.0005). If the trough is being chopped off as it appears then the wi***@ha***ax would be greater than actual, so this could be a source of the discrepancy. Michael From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> I believe that’s one reason. The HITRAN broadening parameters do not depend on the atmospheric composition, so I guess those gamma_air, n_air parameters refer to Earth-like air. There is another component too, the formula we are using in Transit requires the particle’s collision diameters, which are very uncertain for molecules. Sally and I were looking into that for a long time, but could hardly found well-documented values. On Apr 26, 2017, at 10:31 PM, Joe Harrington <jh***@phailto:jh@ph***>> wrote: Some of the HITRAN values are for Earth air, which has a very different --jh-- X-Spam-Status: No, score=-1.9 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] I've been looking more into this and have discussed it with Joe to ensure I am understanding pressure/collisional broadening correctly. Most sources use some form of the rate of collision to determine the Lorentzian HWHM. This depends in part on the size of the molecules. The HITRAN formula does not consider that, so I am fairly certain that it will not be correct in situations with a high collision rate (i.e. Lorentz dominated). Is the collision rate used in transit to calculate the Lorentzian HWHM? If so, where is it calculated or what is referenced for the value? I did a calculation using the equation in the paper you linked; the result is a number far too large to be correct. I'm using cgs units (number density in cm-3, collision diameter in cm, k Boltzmann in erg K-1, temperature in K, mass in g). The number density I calculate is quite large; I am calculating that from the ideal gas law, N/V = P/(kT). As far as I know this should yield the correct number density, but that value is dominating the result so perhaps not. It's also possible that that equation only holds for lower temperatures and breaks do***@th***emperature I am using (1272 K). Also, regarding your Doppler test: For a Lorentzian test, I put the methane layer deeper in the atmosphere (pressure = ~3.35e-1 bars). This produces a line in transit with a FWHM of 0.19 cm-1. Using the HITRAN formula for the Lorentzian HWHM, I find a FWHM that is smaller than transit by a factor of 5. I'm pretty sure this is due to the HITRAN formula not considering the molecule's size which will affect the rate of collisions, as mentioned earlier. Best, From: BART-devel <ba***@phailto:ba@ph***>> on behalf of Patricio Cubillos <pc***@fuailto:pc@fu***>> By the way, there is a typo in Goody (1995), Equation 3.51 for the Lorentz width says n2, but it should read n*sigma2 (at least in the copy I saw). You can contrast this with the equation in this paper: p On Apr 25, 2017, at 1:22 PM, Patricio Cubillos <pc***@fuailto:pc@fu***>mailto:pc***@fu***> wrote: Hi, I would isolate two cases here, one when the broadening is Doppler dominated and another when is Lorentz dominated. Once, one is clear with each case, everything in between should be all right. Doppler is much simpler to test, just go to very low pressures (e.g., 1e-5 bar), there the line profile depends only in T, wn0, and the mass. For your test line, I get a Doppler HWHM = 0.014 cm-1 from Transit, which is consistent with the references you give. So, this part seems to be all right to me (I put my scripts in /home/patricio/ast/esp01/bart/transit/2017-04-27_voigt). Lorentz is more complicated. I have not found any source to confirm the formula, other than Goody (1995) and HITRAN. I have the impression that the HITRAN Lorentz broadening formula refers to air, as in Earth-like atmospheric air. Note that, unlike the equation in Goody (1995), the HITRAN equation does not depend on which is the gas mixture of the atmosphere. And after all, HITRAN was developed thinking on Earth-like atmospheres. I may well be wrong, it might be that all of the necessary info for the pressure broadening is contained in the pressures. But I don’t really know. Best, On Apr 24, 2017, at 9:43 PM, Michael Himes <mh***@knailto:mh@kn***>mailto:mh***@kn***> wrote: Hi, I've been running more tests to try to match the width measured in transit, but I am unable to do so. I'll describe the two methods that have yielded the closest results. For both, I am working in cgs units, and FWHM values are in units of cm-1. In transit, the comparison line has FWHM of 0.0755 cm-1. (To get an accurate value, I lowered the wavenumber sampling interval to the minimum value before the code broke, which was at a value of 0.002). Since I am using a HITRAN line to compare transit to a pre-calculated Voigt function, I used the formulas provided by HITRAN. I assume these equations work properly or else someone would have complained to HITRAN by now. The formulas can be found here http://hitran.org/docs/definitions-and-units/ Using these formulas for alpha and gamma, the resulting Voigt profile has a FWHM of 0.02897 cm-1. I also used a more general equation that could be used for any line list. Those formulas are found in a number of places online; here are two that I referenced: I also referenced An Introduction to Modern Astrophysics by Carroll and Ostlie. In these, the formula given in wavelength space specifies that it is the FWHM, but the formula in frequency space it is not explicitly specified. I assume it is given as the FWHM as well, but in the event that it is not I have also included the resulting value assuming it is the HWHM. I noticed that the wavelength form has a factor of sqrt(ln 2) that the frequency form lacks, so I also tested it with this factor; the resulting FWHM values are a little smaller in this case as expected. Using those formulas, the resulting Voigt profile has a FWHM of 0.02586 cm-1; this is close agreement with the HITRAN method. If the Doppler width is instead given as the HWHM, then the resulting FWHM is 0.042 cm-1. I am more confident in the FWHM value of this method than the HITRAN method since it can be applied to any line list. Both methods are in disagreement with transit by a factor of***@le*** 1.8. I've checked over everything a few times and had a second set of eyes look over it to make sure I am not doing something obviously wrong. If you'd like to take a lo***@it***ourself, see Best, BART-devel mailing list [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list BART-devel mailing list -------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: jh***@ph*** (Joe Harrington) Yes, we compute the line width for a finite interval because of --jh-- X-Spam-Status: No, score=-1.5 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] I don't know about the fl***@th***ottom of the trough, but the cutoff in the wings is, I believe, because we don't bother calculating the profile of each line across the whole spectrum. In theory, every line contributes across the entire spectral range, but in practice this contribution gets very small in the wings. We have to do this calculation tons of times (millions of spectral lines), so we can't afford to consider contributions far from the central peak or we'd be running transit for weeks. So we cut off after some threshold. Patricio, please correct me if I'm wrong. -Ryan From: BART-devel <ba***@ph***> on behalf of Michael Himes <mh***@kn***> I found a test of the Lorentz HWHM in transit/transit/test/lorentz.dat. It uses the collision cross sectional area and calculates a rate of collisions, so I think it should be more accurate than the HITRAN method. Based on the co***@th***nd of the file, it seems that this calculation matches the calculation in transit. Following that method, I calculate a Lorentz HWHM that is ~15% larger than that of the HITRAN method (for p=0.33516 bars, T = 1442.58 K). Based on the calculated alpha and gamma values, the profile should still be Doppler-dominated in the core of the line (alpha is ~1.7x larger). The width in transit is larger by a factor of ~ 5 indicating that gamma and/or alpha in transit is a larger value than what I am calculating. However, my calculated values are almost the exact same as those in transit's output. Transit prints out Lorentz: 8.76413e-03, Doppler: 1.48284e-02 (T=1442.58) My calculated values are Lorentz: 8.7654e-03, Doppler: 1.48322e-02 The slight discrepancy I attribute to using rounded values for constants rather than constants within a Python package such as Scipy. Also, I noticed two things that are a little weird with the line in transit further indicating that something is not quite right. The wings are cut off after a certain point, and the trough of the line is squared off with rounded edges. I had noticed this previously but I thought it was due to the large wavenumber sampling interval. However, the features are still there even with a small sampling interval (0.0005). If the trough is being chopped off as it appears then the wi***@ha***ax would be greater than actual, so this could be a source of the discrepancy. Michael From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> I believe that’s one reason. The HITRAN broadening parameters do not depend on the atmospheric composition, so I guess those gamma_air, n_air parameters refer to Earth-like air. There is another component too, the formula we are using in Transit requires the particle’s collision diameters, which are very uncertain for molecules. Sally and I were looking into that for a long time, but could hardly found well-documented values. On Apr 26, 2017, at 10:31 PM, Joe Harrington <jh***@phailto:jh@ph***>> wrote: Some of the HITRAN values are for Earth air, which has a very different --jh-- X-Spam-Status: No, score=-1.9 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] I've been looking more into this and have discussed it with Joe to ensure I am understanding pressure/collisional broadening correctly. Most sources use some form of the rate of collision to determine the Lorentzian HWHM. This depends in part on the size of the molecules. The HITRAN formula does not consider that, so I am fairly certain that it will not be correct in situations with a high collision rate (i.e. Lorentz dominated). Is the collision rate used in transit to calculate the Lorentzian HWHM? If so, where is it calculated or what is referenced for the value? I did a calculation using the equation in the paper you linked; the result is a number far too large to be correct. I'm using cgs units (number density in cm-3, collision diameter in cm, k Boltzmann in erg K-1, temperature in K, mass in g). The number density I calculate is quite large; I am calculating that from the ideal gas law, N/V = P/(kT). As far as I know this should yield the correct number density, but that value is dominating the result so perhaps not. It's also possible that that equation only holds for lower temperatures and breaks do***@th***emperature I am using (1272 K). Also, regarding your Doppler test: For a Lorentzian test, I put the methane layer deeper in the atmosphere (pressure = ~3.35e-1 bars). This produces a line in transit with a FWHM of 0.19 cm-1. Using the HITRAN formula for the Lorentzian HWHM, I find a FWHM that is smaller than transit by a factor of 5. I'm pretty sure this is due to the HITRAN formula not considering the molecule's size which will affect the rate of collisions, as mentioned earlier. Best, From: BART-devel <ba***@phailto:ba@ph***>> on behalf of Patricio Cubillos <pc***@fuailto:pc@fu***>> By the way, there is a typo in Goody (1995), Equation 3.51 for the Lorentz width says n2, but it should read n*sigma2 (at least in the copy I saw). You can contrast this with the equation in this paper: p On Apr 25, 2017, at 1:22 PM, Patricio Cubillos <pc***@fuailto:pc@fu***>mailto:pc***@fu***> wrote: Hi, I would isolate two cases here, one when the broadening is Doppler dominated and another when is Lorentz dominated. Once, one is clear with each case, everything in between should be all right. Doppler is much simpler to test, just go to very low pressures (e.g., 1e-5 bar), there the line profile depends only in T, wn0, and the mass. For your test line, I get a Doppler HWHM = 0.014 cm-1 from Transit, which is consistent with the references you give. So, this part seems to be all right to me (I put my scripts in /home/patricio/ast/esp01/bart/transit/2017-04-27_voigt). Lorentz is more complicated. I have not found any source to confirm the formula, other than Goody (1995) and HITRAN. I have the impression that the HITRAN Lorentz broadening formula refers to air, as in Earth-like atmospheric air. Note that, unlike the equation in Goody (1995), the HITRAN equation does not depend on which is the gas mixture of the atmosphere. And after all, HITRAN was developed thinking on Earth-like atmospheres. I may well be wrong, it might be that all of the necessary info for the pressure broadening is contained in the pressures. But I don’t really know. Best, On Apr 24, 2017, at 9:43 PM, Michael Himes <mh***@knailto:mh@kn***>mailto:mh***@kn***> wrote: Hi, I've been running more tests to try to match the width measured in transit, but I am unable to do so. I'll describe the two methods that have yielded the closest results. For both, I am working in cgs units, and FWHM values are in units of cm-1. In transit, the comparison line has FWHM of 0.0755 cm-1. (To get an accurate value, I lowered the wavenumber sampling interval to the minimum value before the code broke, which was at a value of 0.002). Since I am using a HITRAN line to compare transit to a pre-calculated Voigt function, I used the formulas provided by HITRAN. I assume these equations work properly or else someone would have complained to HITRAN by now. The formulas can be found here http://hitran.org/docs/definitions-and-units/ Using these formulas for alpha and gamma, the resulting Voigt profile has a FWHM of 0.02897 cm-1. I also used a more general equation that could be used for any line list. Those formulas are found in a number of places online; here are two that I referenced: I also referenced An Introduction to Modern Astrophysics by Carroll and Ostlie. In these, the formula given in wavelength space specifies that it is the FWHM, but the formula in frequency space it is not explicitly specified. I assume it is given as the FWHM as well, but in the event that it is not I have also included the resulting value assuming it is the HWHM. I noticed that the wavelength form has a factor of sqrt(ln 2) that the frequency form lacks, so I also tested it with this factor; the resulting FWHM values are a little smaller in this case as expected. Using those formulas, the resulting Voigt profile has a FWHM of 0.02586 cm-1; this is close agreement with the HITRAN method. If the Doppler width is instead given as the HWHM, then the resulting FWHM is 0.042 cm-1. I am more confident in the FWHM value of this method than the HITRAN method since it can be applied to any line list. Both methods are in disagreement with transit by a factor of***@le*** 1.8. I've checked over everything a few times and had a second set of eyes look over it to make sure I am not doing something obviously wrong. If you'd like to take a lo***@it***ourself, see Best, BART-devel mailing list [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list BART-devel mailing list [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list |
Beta Was this translation helpful? Give feedback.
-
|
From: pc***@fu*** (Patricio Cubillos)
The thing with the center of the line depends on which atmosphere you are using. If I had to guess, it seems that you have a non-inverted atmosphere, where the core of the line is ’saturating’ the absorption. So you see the brightness temperature of the top of the at***@th***enter of the line. Best, |
Beta Was this translation helpful? Give feedback.
-
|
From: mh***@kn*** (Michael Himes) Yes, I am using a non-inverted atmosphere. I went ahead and found the width of the trough, then found the value in the calculated profile where the width was equal to that, and then found the wi***@ha***f that value. The result is smaller than the width in transit by roughly a factor of 2, so it seems that the saturation you mention isn't quite so simple. I'm not familiar with the physics of line saturation, and in researching about spectral line broadening I hadn't come across anything about that. Do you have a good resource to learn about this? I've started looking around but have not found much of use. It may be possible to simulate saturation in the calculated profile; this could confirm both the proper width/shape of the line as well as the saturation of the line. Alternatively, is there a particular PT profile that would not exhibit saturation of lines so that the width/shape could be tested in a straight-forward manner? In this case I think simulating the saturation would still be a good thing to test to ensure that that part is correct as well. Michael From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> On Apr 28, 2017, at 2:58 AM, Joe Harrington <jh***@phailto:jh@ph***>> wrote: Yes, we compute the line width for a finite interval because of I don't know about the fl***@th***ottom of the trough, but the cutoff in the wings is, I believe, because we don't bother calculating the profile of each line across the whole spectrum. In theory, every line contributes across the entire spectral range, but in practice this contribution gets very small in the wings. We have to do this calculation tons of times (millions of spectral lines), so we can't afford to consider contributions far from the central peak or we'd be running transit for weeks. So we cut off after some threshold. Patricio, please correct me if I’m wrong. The thing with the center of the line depends on which atmosphere you are using. If I had to guess, it seems that you have a non-inverted atmosphere, where the core of the line is ’saturating’ the absorption. So you see the brightness temperature of the top of the at***@th***enter of the line. Best, |
Beta Was this translation helpful? Give feedback.
-
|
From: jh***@ph*** (Joe Harrington) Line saturation is pretty straightforward. The transmission is The net effect of saturation is to make the line more square-shaped, so So, reduce the density or opacity, or make the layer thinner. A factor For emission, there is absorption by the same line that emitted, all the A good test might have a hot interior and a thin, high, cold layer, and --jh-- From: Michael Himes <mh***@kn***> [1:multipart/alternative Hide] [1/1:text/plain Hide] Yes, I am using a non-inverted atmosphere. I went ahead and found the width of the trough, then found the value in the calculated profile where the width was equal to that, and then found the wi***@ha***f that value. The result is smaller than the width in transit by roughly a factor of 2, so it seems that the saturation you mention isn't quite so simple. I'm not familiar with the physics of line saturation, and in researching about spectral line broadening I hadn't come across anything about that. Do you have a good resource to learn about this? I've started looking around but have not found much of use. It may be possible to simulate saturation in the calculated profile; this could confirm both the proper width/shape of the line as well as the saturation of the line. Alternatively, is there a particular PT profile that would not exhibit saturation of lines so that the width/shape could be tested in a straight-forward manner? In this case I think simulating the saturation would still be a good thing to test to ensure that that part is correct as well. Michael From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> On Apr 28, 2017, at 2:58 AM, Joe Harrington <jh***@phailto:jh@ph***>> wrote: Yes, we compute the line width for a finite interval because of I don't know about the fl***@th***ottom of the trough, but the cutoff in the wings is, I believe, because we don't bother calculating the profile of each line across the whole spectrum. In theory, every line contributes across the entire spectral range, but in practice this contribution gets very small in the wings. We have to do this calculation tons of times (millions of spectral lines), so we can't afford to consider contributions far from the central peak or we'd be running transit for weeks. So we cut off after some threshold. Patricio, please correct me if I’m wrong. The thing with the center of the line depends on which atmosphere you are using. If I had to guess, it seems that you have a non-inverted atmosphere, where the core of the line is ’saturating’ the absorption. So you see the brightness temperature of the top of the at***@th***enter of the line. Best, [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list |
Beta Was this translation helpful? Give feedback.
-
|
From: mh***@kn*** (Michael Himes) (message from Michael Himes on Fri, 28 Apr 2017 19:18:29 Between that explanation and a couple of other sources (Carroll & Ostlie, and http://spiff.rit.edu/classes/phys440/lectures/curve/curve.html ) I feel like I have a good grasp on line saturation conceptually, but I'm still not totally seeing the mathematical connection to the shape of the observed line besides the increase in effective width. I ran some more tests with varying abundances. In the following cases I used nitrogen to fill the rest of the layer. Reducing the abundance from 100% to 10% reduced the saturation effect, but it was still present (FWHM = 0.065 cm-1 in transit). The line no longer appears saturated when I reduce the abundance to 1%, and the measured FWHM is within 3% of the calculated FWHM (0.0394 cm-1 in transit, vs 0.0405 cm-1 calculated). Since it no longer appeared saturated, I thought that further reducing the abundance would only affect the line depth without changing the FWHM (much like multiplying the calculated profile by a constant doesn't change the FWHM). However, when I reduce the abundance to 0.1%, the FWHM decreases to 0.0352 cm-1. Reducing it by another factor of 10 reduces the FWHM a little bit more to 0.0347 cm-1. I'm not sure if this is due to the low abundance (and thus is expected), or if it is because the line was still somewhat saturated at 1% abundance but did not appear that way. I also tried manually reducing the layer thickness by a factor of 10, but that turned the absorption line into a very, very, very intense emission line (on the order of 1e300). I'm guessing that this result is because the radii no longer properly satisfy the hyodrostatic equilibrium equation if I do that. Michael From: BART-devel <ba***@ph***> on behalf of Joe Harrington <jh***@ph***> Line saturation is pretty straightforward. The transmission is The net effect of saturation is to make the line more square-shaped, so So, reduce the density or opacity, or make the layer thinner. A factor For emission, there is absorption by the same line that emitted, all the A good test might have a hot interior and a thin, high, cold layer, and --jh-- From: Michael Himes <mh***@kn***> [1:multipart/alternative Hide] [1/1:text/plain Hide] Yes, I am using a non-inverted atmosphere. I went ahead and found the width of the trough, then found the value in the calculated profile where the width was equal to that, and then found the wi***@ha***f that value. The result is smaller than the width in transit by roughly a factor of 2, so it seems that the saturation you mention isn't quite so simple. I'm not familiar with the physics of line saturation, and in researching about spectral line broadening I hadn't come across anything about that. Do you have a good resource to learn about this? I've started looking around but have not found much of use. It may be possible to simulate saturation in the calculated profile; this could confirm both the proper width/shape of the line as well as the saturation of the line. Alternatively, is there a particular PT profile that would not exhibit saturation of lines so that the width/shape could be tested in a straight-forward manner? In this case I think simulating the saturation would still be a good thing to test to ensure that that part is correct as well. Michael From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> On Apr 28, 2017, at 2:58 AM, Joe Harrington <jh***@phailto:jh@ph***>> wrote: Yes, we compute the line width for a finite interval because of I don't know about the fl***@th***ottom of the trough, but the cutoff in the wings is, I believe, because we don't bother calculating the profile of each line across the whole spectrum. In theory, every line contributes across the entire spectral range, but in practice this contribution gets very small in the wings. We have to do this calculation tons of times (millions of spectral lines), so we can't afford to consider contributions far from the central peak or we'd be running transit for weeks. So we cut off after some threshold. Patricio, please correct me if I’m wrong. The thing with the center of the line depends on which atmosphere you are using. If I had to guess, it seems that you have a non-inverted atmosphere, where the core of the line is ’saturating’ the absorption. So you see the brightness temperature of the top of the at***@th***enter of the line. Best, [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list BART-devel mailing list -------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: pc***@fu*** (Patricio Cubillos) If you are only focus on the shape of a line profile, I suggest to lo***@th***xtinction coefficient array rather than the flux spectrum. The former should keep exactly the shape of the Voigt profile, regardless of the geometry or atmosphere. Best,
-------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: jh***@ph*** (Joe Harrington) Since the peak is depressed, the point on the curve that's identified as Patricio makes a good point (and I said something similar last week). Since you're in this deep, why not buy the textbook to our class, --jh-- X-Spam-Status: No, score=-1.5 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] If you are only focus on the shape of a line profile, I suggest to lo***@th***xtinction coefficient array rather than the flux spectrum. The former should keep exactly the shape of the Voigt profile, regardless of the geometry or atmosphere. Best,
[1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list |
Beta Was this translation helpful? Give feedback.
-
|
From: mh***@kn*** (Michael Himes) (message from Michael Himes on Tue, 2 May 2017 05:26:36 Oh, I see the issue now. I'll start by comparing the opacity array to the calculated Voigt profile as that should be relatively quick. I'll purchase that textbook when I return from Europe, I'm sure it will help my understanding a lot. Michael From: Joe Harrington <jh***@ph***> Since the peak is depressed, the point on the curve that's identified as Patricio makes a good point (and I said something similar last week). Since you're in this deep, why not buy the textbook to our class, --jh-- X-Spam-Status: No, score=-1.5 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] If you are only focus on the shape of a line profile, I suggest to lo***@th***xtinction coefficient array rather than the flux spectrum. The former should keep exactly the shape of the Voigt profile, regardless of the geometry or atmosphere. Best,
[1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list |
Beta Was this translation helpful? Give feedback.
-
|
From: mh***@kn*** (Michael Himes) (message from Michael Himes on Tue, 2 May 2017 05:26:36 I haven't yet learned enough to simulate saturation, but I have compared the opacity array to the calculated Voigt profile.
It's possible that this disagreement is due to how I am calculating alpha and gamma for the Voigt profile. Alpha is via HITRAN's supplied equation, and gamma is calculated based on transit/transit/test/lorentz.dat. I have found both equations in other sources as well. I wrote 2 scripts to demonstrate how these values are being calculated if you would like to take a look. They are located at Michael From: BART-devel <ba***@ph***> on behalf of Michael Himes <mh***@kn***> Oh, I see the issue now. I'll start by comparing the opacity array to the calculated Voigt profile as that should be relatively quick. I'll purchase that textbook when I return from Europe, I'm sure it will help my understanding a lot. Michael From: Joe Harrington <jh***@ph***> Since the peak is depressed, the point on the curve that's identified as Patricio makes a good point (and I said something similar last week). Since you're in this deep, why not buy the textbook to our class, --jh-- X-Spam-Status: No, score=-1.5 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] If you are only focus on the shape of a line profile, I suggest to lo***@th***xtinction coefficient array rather than the flux spectrum. The former should keep exactly the shape of the Voigt profile, regardless of the geometry or atmosphere. Best,
[1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list |
Beta Was this translation helpful? Give feedback.
-
|
From: pc***@fu*** (Patricio Cubillos) Hi Michael, I’d say the differences come from approximations in the code. Even though a layer have specific {p,T}, Transit uses approximate values to the HW’s. It goes a bit like this:
With your script, If you computed the profile using the HW values that Transit uses (for your layer: Dop HW=0.01473, Lor HW=0.00464), you can reproduce the line’s FWHM of ~0.035 (all units are cm-1). If you plot the profiles, you’ll see that they match pretty well (red and green curves): Best,
-------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: mh***@kn*** (Michael Himes) Patricio, Does this approximation negligibly affect the result? The shape is obviously different, but you mentioned that the magnitude is conserved so it sounds like it doesn't affect things much if***@al***f this is the case, then I think it would be good to mention/explain this in one of the papers if it isn't already. As for the FW calculation, I wanted to interpolate to find a more accurate value. I suppose it didn't affect the result much. I compared the results of transit to the data Ian and Jasmina sent. I believe I have everything set up correctly, but the results are quite different.
Michael From: BART-devel <ba***@ph***> on behalf of Patricio Cubillos <pc***@fu***> Hi Michael, I’d say the differences come from approximations in the code. Even though a layer have specific {p,T}, Transit uses approximate values to the HW’s. It goes a bit like this:
With your script, If you computed the profile using the HW values that Transit uses (for your layer: Dop HW=0.01473, Lor HW=0.00464), you can reproduce the line’s FWHM of ~0.035 (all units are cm-1). If you plot the profiles, you’ll see that they match pretty well (red and green curves): Best, On Jun 1, 2017, at 9:57 PM, Michael Himes <mh***@knailto:mh@kn***>> wrote: I haven't yet learned enough to simulate saturation, but I have compared the opacity array to the calculated Voigt profile.
It's possible that this disagreement is due to how I am calculating alpha and gamma for the Voigt profile. Alpha is via HITRAN's supplied equation, and gamma is calculated based on transit/transit/test/lorentz.dat. I have found both equations in other sources as well. I wrote 2 scripts to demonstrate how these values are being calculated if you would like to take a look. They are located at Michael From: BART-devel <ba***@phailto:ba@ph***>> on behalf of Michael Himes <mh***@knailto:mh@kn***>> Oh, I see the issue now. I'll start by comparing the opacity array to the calculated Voigt profile as that should be relatively quick. I'll purchase that textbook when I return from Europe, I'm sure it will help my understanding a lot. Michael From: Joe Harrington <jh***@phailto:jh@ph***>> Since the peak is depressed, the point on the curve that's identified as Patricio makes a good point (and I said something similar last week). Since you're in this deep, why not buy the textbook to our class, --jh-- X-Spam-Status: No, score=-1.5 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide] If you are only focus on the shape of a line profile, I suggest to lo***@th***xtinction coefficient array rather than the flux spectrum. The former should keep exactly the shape of the Voigt profile, regardless of the geometry or atmosphere. Best,
[1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list BART-devel mailing list -------------- next part -------------- |
Beta Was this translation helpful? Give feedback.
-
|
From: pc***@fu*** (Patricio Cubillos)
This depends on what data are you modeling (or what spectral resolution you are aiming). Take WFC3 for example, there you have a resolution of R~60, th***@1.***m you have a resolving power of about 6667/60 cm-1 = ~100 cm-1. So, this is four orders of magnitude larger than the difference. Of course, if you plan to model high-res data or consider other more exotic issues (e.g., http://adsabs.harvard.edu/abs/2017ApJ...841L...3D) you need to be more careful. Best, |
Beta Was this translation helpful? Give feedback.
-
|
From: jh***@ph*** (Joe Harrington) Michael, could you go into the transit user doc, find the right place(s) Thanks, --jh-- X-Spam-Status: No, score=-1.9 required=3.0 tests=BAYES_00,HTML_MESSAGE, [1:multipart/alternative Hide] [1/1:text/plain Hide]
This depends on what data are you modeling (or what spectral resolution you are aiming). Take WFC3 for example, there you have a resolution of R~60, th***@1.***m you have a resolving power of about 6667/60 cm-1 = ~100 cm-1. So, this is four orders of magnitude larger than the difference. Of course, if you plan to model high-res data or consider other more exotic issues (e.g., http://adsabs.harvard.edu/abs/2017ApJ...841L...3D) you need to be more careful. Best, [1/2:text/html Show] [2:text/plain Hide] BART-devel mailing list |
Beta Was this translation helpful? Give feedback.
-
The following is an archived message from the BART-devel mailing list, which has now closed.
From: mh***@kn*** (Michael Himes)
Date: Mon, 24 Apr 2017 19:43:26 +0000
Subject: [BART-devel] Voigt profile width
Hi,
I've been running more tests to try to match the width measured in transit, but I am unable to do so. I'll describe the two methods that have yielded the closest results. For both, I am working in cgs units, and FWHM values are in units of cm-1. In transit, the comparison line has FWHM of 0.0755 cm-1. (To get an accurate value, I lowered the wavenumber sampling interval to the minimum value before the code broke, which was at a value of 0.002).
Since I am using a HITRAN line to compare transit to a pre-calculated Voigt function, I used the formulas provided by HITRAN. I assume these equations work properly or else someone would have complained to HITRAN by now. The formulas can be found here http://hitran.org/docs/definitions-and-units/
Using these formulas for alpha and gamma, the resulting Voigt profile has a FWHM of 0.02897 cm-1.
I also used a more general equation that could be used for any line list. Those formulas are found in a number of places online; here are two that I referenced:
http://www-star.st-and.ac.uk/~kw25/teaching/nebulae/lecture08_linewidths.pdf
http://www.phy.ohiou.edu/~mboett/astro401_fall12/broadening.pdf
I also referenced An Introduction to Modern Astrophysics by Carroll and Ostlie. In these, the formula given in wavelength space specifies that it is the FWHM, but the formula in frequency space it is not explicitly specified. I assume it is given as the FWHM as well, but in the event that it is not I have also included the resulting value assuming it is the HWHM. I noticed that the wavelength form has a factor of sqrt(ln 2) that the frequency form lacks, so I also tested it with this factor; the resulting FWHM values are a little smaller in this case as expected.
Using those formulas, the resulting Voigt profile has a FWHM of 0.02586 cm-1; this is close agreement with the HITRAN method. If the Doppler width is instead given as the HWHM, then the resulting FWHM is 0.042 cm-1.
I am more confident in the FWHM value of this method than the HITRAN method since it can be applied to any line list. Both methods are in disagreement with transit by a factor of***@le*** 1.8. I've checked over everything a few times and had a second set of eyes look over it to make sure I am not doing something obviously wrong. If you'd like to take a lo***@it***ourself, see
/home/mhimes/retrievaltests/voigt-calc/calcprof.py
Best,
Michael
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://physics.ucf.edu/pipermail/bart-devel/attachments/20170424/087134bb/attachment.html
Beta Was this translation helpful? Give feedback.
All reactions