Pith. sign in

REVIEW 3 major objections 3 minor 50 references

The Dust in M31

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Standard dust models overpredict M31 starlight absorption by at least a factor of 2.5.

desk verdict A careful measurement paper whose most novel claim—the R–beta anti-correlation—needs a synthetic joint-recovery test before it can be used as a dust-model constraint. read the letter →

arxiv 1908.03458 v1 pith:5NSSDFYK submitted 2019-08-09 astro-ph.GA

Ant Whitworth (Cardiff) , Ken Marsh (CalTech) , Phil Cigan (Cardiff) , Julianne Dalcanton (Washington) , Matt Smith (Cardiff) , Haley Gomez (Cardiff) , Olly Lomax (ESA , Noordwijk)
show 2 more authors
Matt Griffin (Cardiff) Steve Eales (Cardiff)
This is my paper · ORCID
classification astro-ph.GA
keywords interstellardustM31opticaldepthfar-infraredemissionnear-infraredextinctionmodelsemissivityindexredgiantbranchstars
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using far-infrared images analysed with the ppmap image-reconstruction procedure, this paper compares, pixel by pixel, the dust optical depth at 300 µm that emits in the far-infrared with the dust optical depth at 1.1 µm that extinguishes near-infrared starlight in the Andromeda galaxy (M31). The observed ratio $R_{\rm obs}=\tau_{1.1}/\tau_{300}$ falls between 500 and 1500, whereas standard theoretical dust models predict $\kappa_{1.1}/\kappa_{300}$ in the range 2500 to 4000. The paper argues that this gap is not a measurement artifact: the far-infrared optical depth agrees with an independent analysis, and two analytic arguments suggest that at least 60% of the 300 µm-emitting dust cannot be hidden in compact sources that never intercept the line of sight to the red giant branch stars used for extinction. It concludes that dust models may need revision, and it reports a new empirical anti-correlation, $R_{\rm obs}\simeq 2042(\pm24)-557(\pm10)\bar{\beta}$, that any revised model must reproduce.

What carries the argument

The load-bearing object is the ratio $R=\tau_{1.1}/\tau_{300}$, comparing a near-infrared extinction optical depth at 1.1 µm with a far-infrared emission optical depth at 300 µm on matched 31 pc pixels; its model counterpart is $R_{\rm model}=\kappa_{1.1}/\kappa_{300}$, computed from the dust opacity coefficients of candidate grain models. The comparison is made possible by the ppmap procedure, a Bayesian image-reconstruction method that separates the 300 µm optical depth into emissivity-index and temperature bins and yields the optical-depth-weighted mean emissivity index $\bar{\beta}$, and by a near-infrared extinction map from the reddening of red giant branch stars that provides $\tau_{1.1}$. Two analytic distributions carry the compact-source argument: a log-normal column-density PDF with a single power-law tail (Eq. 6.2) and a turbulent core mass function $dN/dm\propto m^{-7/3}$ (Eq. 6.5). The newly reported result is the linear relation $R_{\rm obs}\simeq 2042(\pm24)-557(\pm10)\bar{\beta}$ (Eq. 5.2).

What would settle it

Point a far-infrared interferometer or a few-pc-resolution sub-millimetre camera at one of M31's star-forming rings and measure how much of the 300 µm flux comes from compact, unresolved cores; if more than 60% of the emission is in sources that are too small to lie in front of the red giant branch stars, Explanation B is restored and the central claim collapses. Equivalently, a measurement of the column-density PDF at pc resolution showing a prominent power-law tail with $\alpha<1.5$ and $\varphi>0.5$ would also revive the compact-source explanation.

Watch

Extended reading notes

Core claim

The central claim is that the dust in M31 absorbs and emits with an opacity ratio that is incompatible with the bulk of current theoretical dust models, and that the incompatibility is real rather than a measurement artifact. On the same 31 pc scale, $R_{\rm obs}\equiv\tau_{1.1}/\tau_{300}$ sits at 500–1500, whereas the model ratio $R_{\rm model}\equiv\kappa_{1.1}/\kappa_{300}$ is 2500–4000; only one observationally calibrated model comes close to the observed values. The paper finds that the far-infrared optical depth $\tau_{300}$ is consistent with an independent, completely different analysis, so Explanation A is unlikely; and it presents two analytic arguments—one based on the tail of the column-density probability distribution, one based on the turbulent core mass function—to show that hiding at least 60% of the 300 µm-emitting dust in compact sources is implausible. Consequently the real possibility is Explanation C: existing dust models need revision. In addition, the paper establishes an empirical anti-correlation between $R_{\rm obs}$ and the optical-depth-weighted mean emissivity index, Eq. (5.2), which any revised model would have to reproduce.

Load-bearing premise

The load-bearing premise is that the compact dust population in M31 can be described by a log-normal column-density PDF with a single power-law tail and by a turbulent core mass function $dN/dm\propto m^{-7/3}$; if the real compact dust has a different distribution, the conclusion that at least 60% of the far-infrared-emitting dust cannot hide in compact sources would not follow.

Editorial extensions

If this is right

  • If the discrepancy is real, the far-infrared mass opacity $\kappa_{300}$ in standard dust models must be roughly a factor 2.5 higher (or $\kappa_{1.1}$ lower) to match M31, so dust masses derived from far-infrared fluxes of external galaxies would shrink correspondingly.
  • Smaller far-infrared-derived dust masses would relax the requirement for extremely rapid dust formation in high-redshift galaxies.
  • Revised dust models must explain both observed locations $(\bar{\beta},R_{\rm obs})\sim(2.0,\,1000)$ and $(2.5,\,500)$ in the ratio–emissivity plane; the second location is not covered by any commonly used model.
  • The anti-correlation $R_{\rm obs}=2042(\pm24)-557(\pm10)\bar{\beta}$ provides a direct, quantitative test target for dust models, and the paper's single-size grain grid identifies a few minerals that populate the high-$\bar{\beta}$, low-$R$ end.
  • The result extends the known dust energy balance problem to a galaxy-wide, resolved scale, pointing to a common origin in dust models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If confirmed, the anti-correlation could be used as an environmental probe: measuring $R_{\rm obs}$ in other nearby galaxies might trace where grain growth, destruction, or coagulation shifts the dust population along the $\bar{\beta}$–$R$ relation.
  • The same pixel-scale comparison could be made inside the Milky Way with infrared extinction surveys and far-infrared emission maps; a similar low ratio would show that the model deficit is universal, while a higher ratio would single out M31's conditions.
  • The compact-source rejection depends on two idealized distribution shapes; direct sub-arcsecond far-infrared imaging of an M31 star-forming ring is a concrete, decisive test of whether more than 60% of the 300 µm flux is confined to unresolved cores.
  • One testable extension of Eq. (5.2) is to predict the ratio at other wavelengths, e.g. comparing $\tau_{1.1}$ with $\tau_{250}$ or $\tau_{500}$, which would tell whether the model shortfall is a special property of the 300 µm opacity or a general far-infrared error.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper applies the PPMAP Bayesian deconvolution procedure to Herschel PACS/SPIRE maps of M31 to derive maps of the 300-micron emission optical depth tau_300, the optical-depth-weighted mean emissivity index betabar, and the dust temperature Tbar at roughly 31 pc resolution. Combining tau_300 with the near-IR extinction optical depth tau_1.1 from Dalcanton et al. (2015), the authors measure the ratio R_obs = tau_1.1/tau_300 and find values in the range 500-1500, well below theoretical model values R_model = kappa_1.1/kappa_300 of roughly 2500-4000. They argue that Explanation A, namely that tau_300 is inaccurate, is unlikely because the PPMAP results agree with those of Draine et al. (2014), and they present two analytic arguments against Explanation B, namely that a large fraction of the emitting dust is hidden in compact sources. The paper therefore concludes that existing dust models may need revision. It also reports a new anti-correlation, R_obs = 2042 +/- 24 - (557 +/- 10) betabar (Eq. 5.2), which it presents as a challenging constraint on interstellar dust models.

Significance. If the central claims hold, the paper provides a valuable local-Universe constraint on dust emission models and contributes to the well-known dust energy balance problem. The empirical comparison is careful in several respects: tau_1.1 comes from an independent external analysis, tau_300 is cross-checked against the independent Draine et al. (2014) radial profiles, and a wide range of literature dust models is tabulated for comparison. The claimed R_obs-betabar anti-correlation, if real, would be a sharp new constraint on the mixing of dust populations in M31. However, the new anti-correlation is derived from PPMAP products on both axes and is not supported by a synthetic joint-recovery test, and the two arguments against compact dust sources rely on idealized functional forms. The central conclusion is therefore defensible but not yet fully secured.

major comments (3)
  1. [Section 5, Eq. (5.2)] The anti-correlation R_obs = 2042 - 557 betabar is computed from PPMAP-derived quantities on both axes: R_obs has tau_300 in the denominator, and betabar is a tau_300-weighted mean over the same 48 (beta,T) components. Any PPMAP reconstruction error that redistributes optical depth among beta bins will change tau_300 and betabar jointly, and the well-known beta-T degeneracy could plausibly produce a spurious slope of this sign. The paper quotes uncertainties on betabar (~0.1) and Tbar (~3%) from separate tests, but it does not show that the joint recovery of (tau_300, betabar) is unbiased, nor that an input model with no intrinsic R-beta anti-correlation would not recover a slope near -557. Because Eq. (5.2) is presented as the paper's new challenging constraint, this missing synthetic test is load-bearing and should be supplied.
  2. [Section 6.1, Eq. (6.2)] The argument that compact sources cannot hide at least 60% of the emitting dust depends on assuming a column-density PDF that is a boxcar log-normal plus a single power-law tail with parameters (sigma, phi, alpha). As written, Eq. (6.2) is internally inconsistent: eta = Sigma/tildeSigma is a positive-definite quantity, yet the boxcar extends to eta = -sigma. If eta is intended to be ln(Sigma/tildeSigma), the PDF and the ratios in Eqs. (6.3)-(6.4) need to be re-derived. More importantly, a different compact-source population—one whose clump mass function does not produce a simple power-law tail, or one with a different relation between column density and far-IR emission—would not be excluded by this argument, so Explanation B would remain viable.
  3. [Section 6.2, Eq. (6.5)] The second argument assumes the turbulent-core mass function dN/dm proportional to m^(-7/3) holds down to arbitrarily small masses and equates compact far-IR emitters with non-prestellar cores. The deduced limit m_MIN <~ 8e-7 solar masses (Eq. 6.10) follows from combining this mass function with a Milky Way high-mass star formation rate applied to M31. If the actual compact dust population is not described by this core mass function—for example, if it consists of unresolved clumps with a different mass spectrum—the claimed unlikelihood of Explanation B does not follow. The argument should be tied more directly to M31's observed core and star-formation properties, or its sensitivity to the assumed mass function should be demonstrated.
minor comments (3)
  1. [Section 4, text near Fig. 4] The text 'the map at beta2 = 2.0 K actually represents dust...' should read 'beta2 = 2.0' rather than '2.0 K', since K is a temperature unit and does not apply to the emissivity index.
  2. [Section 5, discussion of Fig. 7] The statement that 'the ppmap results are essentially model independent' is too strong; PPMAP still assumes optically thin emission, a discrete beta grid, and beta independent of T, as described in Section 3. The wording should be tempered to 'relatively free of the assumptions of the standard single-temperature fit.'
  3. [Figure 5 caption] The x-axis label in the caption reads 'beta, beta'; it should be a single symbol, presumably betabar, to avoid confusion with the beta values of the theoretical models.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central ratio uses an independent near-IR extinction map, and Eq. 5.2 is an empirical fit rather than a construction from the model inputs.

full rationale

The paper's main claim compares tau_1.1 from Dalcanton et al. (2015) with tau_300 from PPMAP. tau_1.1 is an external, independent data product, and the PPMAP tau_300 map is cross-checked against the independent Draine et al. (2014) analysis. The theoretical R_model values are taken from published dust models (Table 2 and Appendix D), not derived in this paper. The anti-correlation R_obs = 2042 - 557 betabar (Eq. 5.2) is presented as a least-squares fit to the pixel data; it is not obtained by substituting the definition of betabar into R_obs, and no equation in the paper reduces R to betabar by construction. The PPMAP method is self-cited (Marsh et al. 2015, 2018), but the current paper does not rely on an unverified assertion from those papers: PPMAP is a separately published procedure and its output is compared with an independent algorithm. The lack of a synthetic joint-recovery test for R and betabar is a potential systematic-uncertainty concern, but it is not a logical circularity under the standards of this analysis.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central claim depends on the PPMAP reconstruction being unbiased and on the two analytic arguments in Section 6, which introduce several modeling choices (boxcar log-normal, power-law tail, turbulent core mass function). The paper is transparent about most assumptions. No invented entities are introduced.

free parameters (5)
  • PPMAP beta grid boundaries and spacing = beta in [1.25, 3.25]; discrete values 1.5, 2.0, 2.5, 3.0
    Chosen by hand to cover the range of inferred betabar (Section 3.3). If real dust had beta outside this range, tau_300 could be biased.
  • PPMAP temperature grid boundaries and spacing = T in [9.3 K, 53.8 K]; twelve log-spaced values 10.0 to 50.0 K
    Chosen by hand; cold dust below 9.3 K would be missed, potentially underestimating tau_300 and inflating the discrepancy.
  • PPMAP stopping criterion = global reduced chi-squared just below 1.0
    Iterations stopped when global reduced chi2 < 1; this tuning affects the reconstructed optical depths (Section 3.2).
  • Linear regression coefficients in Eq. 5.2 = intercept 2042 +/- 24, slope -557 +/- 10
    Ordinary least squares fit to 28,726 pixel values; the reported anti-correlation depends on this fit.
  • 5-sigma detection threshold = >5 sigma in each Herschel band and in tau_1.1
    Pixels below threshold excluded, which may bias the correlation toward brighter, denser regions (acknowledged in Section 5).
assumptions (7)
  • domain assumption Far-IR dust emission is optically thin along the analyzed lines of sight
    PPMAP assumes optically thin emission (Section 3.1); verified post hoc with tau_300 < 0.001 (Section 5).
  • domain assumption Dust far-IR opacity follows a power law with a single emissivity index beta per dust component, and beta is independent of temperature
    Used in the PPMAP forward model (Eqs. 3.3-3.4); limitation (iv) in Section 3.4.
  • domain assumption tau_1.1 from Dalcanton et al. (2015) measures the total line-of-sight dust column, assuming a log-normal distribution of extinctions and a dust scale height much smaller than the RGB star scale height
    External measurement relied on for R_obs; assumptions described in Appendix B and conclusion (ix).
  • ad hoc to paper The column-density PDF is well approximated by a log-normal (replaced by a boxcar) plus a single power-law tail with parameters (sigma, phi, alpha)
    Idealized distribution used in Section 6.1 to derive Eqs. 6.3-6.4; not directly measured.
  • domain assumption The turbulent core mass function follows dN/dm proportional to m^{-7/3} and essentially all high-mass cores form high-mass stars
    Taken from Padoan & Nordlund (2002); used in Section 6.2 to constrain m_MIN.
  • domain assumption M31 distance is 0.78 Mpc
    Used to convert angular scales to physical scales (Section 1.2).
  • domain assumption The conversion factors A_1.1 = 0.3266 A_V and A_1.6 = 0.2029 A_V hold for the RGB population
    Adopted from Dalcanton et al. (2015) to convert color excess to extinction optical depth (Appendix B).

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Dust in M31." pith.science (2026). https://pith.science/paper/5NSSDFYK

@misc{pith2026190803458,
  author       = {Pith},
  title        = {Pith review of: The Dust in M31},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5NSSDFYK}},
  note         = {Machine review of arXiv:1908.03458}
}
read the original abstract

We have analysed Herschel observations of M31, using the PPMAP procedure. The resolution of PPMAP images is sufficient (31 pc on M31) that we can analyse far-IR dust emission on the scale of Giant Molecular Clouds. By comparing PPMAP estimates of the far-IR emission optical depth at 300 microns (tau_300), and the near-IR extinction optical depth at 1.1 microns (tau_1.1) obtained from the reddening of RGB stars, we show that the ratio R_OBS.tau = tau_1.1/tau_300 falls in the range 500 to 1500. Such low values are incompatible with many commonly used theoretical dust models, which predict values of R_MODEL.kappa = kappa_1.1/kappa_300 (where kappa is the dust opacity coefficient) in the range 2500 to 4000. That is, unless a large fraction, at least 60%, of the dust emitting at 300 microns is in such compact sources that they are unlikely to intercept the lines of sight to a distributed population like RGB stars. This is not a new result: variants obtained using different observations and/or different wavelengths have already been reported by other studies. We present two analytic arguments for why it is unlikely that at least 60% of the emitting dust is in sufficiently compact sources. Therefore it may be necessary to explore the possibility that the discrepancy between observed values of R_OBS.tau and theoretical values of R_MODEL.kappa is due to limitations in existing dust models. PPMAP also allows us to derive optical-depth weighted mean values for the emissivity index, beta = - dln(kappa_lambda)/dln(lambda), and the dust temperature, T, denoted betabar and Tbar. We show that, in M31, R_OBS.tau is anti-correlated with betabar according to R_OBS.tau = 2042(+/-24)-557(+/-10)betabar. If confirmed, this provides a challenging constraint on the nature of interstellar dust in M31.

Figures

Figures reproduced from arXiv: 1908.03458 by the authors.

Figure 1
Figure 1. Maps of the ZoomZone, a square 2.7 kpc × 2.7 kpc region at the north-east extremity of the 11 kpc ring. The axes of the ZoomZone are aligned with equatorial coordinates: north is up, east to the left. Its centre is at RA = 11.3499 hr, Dec = 41.9050 deg (J2000). The ZoomZone is also marked with a black square on [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. ppmap images of the whole of M31: (a) total far-IR optical depth at 300 µm, τ300 , (b) mean emissivity index, β¯, and (c) mean dust temperature, T¯. On Panel (a), the black square delineates the region illustrated on [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Images of ∆τ300:` (Eqn. 4.1), i.e. the contribution to the optical depth of dust at 300 µm from dust at the twelve discrete temperatures, T` , used by ppmap. On each panel, T` is marked in the top right corner [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Images of ∆τ300:k (Eqn. 4.2), i.e. the contribution to the optical depth of dust at 300 µm from dust at the four discrete emissivity indices, βk , used by ppmap. On each panel, βk is marked in the top right corner. of R model κ = κ1.1 κ300 (5.3) for several commonly us…
Figure 5
Figure 5. Figure 5: Plot of Robs. τ = τ1.1 /τ300 (Eqn. 5.1) against β¯ (Eqn. 4.4) for the 28726 ppmap pixels that have robust (>5σ) detections; each pixel is represented by a small black dot. The red diamonds and error bars show the means and standard deviations in finite bins, β¯ ± 0.05.…
Figure 6
Figure 6. Figure 6: Correlations between the values of τ300 , β¯, T¯ and Robs. in all pixels where there is a robust (> 5σ) signal. The Pearson correlation coefficients are marked in the top righthand corner of each panel. Contours go down from the peak, NPEAK , by successive factors of 2…
Figure 7
Figure 7. Figure 7: Radial profiles of (a) the total optical depth at 300 µm, τ300 (r); (b) the mean emissivity index, β¯(r); (c) the mean dust temperature, T¯(r); and (d) the ratio of optical depths at 1.1 µm and 300 µm, Robs. τ (r), where r is galactocentric radius. The small black dots…
Figure 8
Figure 8. Figure 8: The filled circles give values of β and Rmodel κ for the tabulated dust models from [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

50 extracted references · 46 canonical work pages

  1. [1]

    C., Gordon K

    Clayton G. C., Gordon K. D., Bianchi L. C., Massa D. L., Fitzpatrick E. L., Bohlin R. C., Wolff M. J., 2015, , 815, 14

    work page 2015

  2. [2]

    Dalcanton J. J. et al. , 2015, , 814, 3

    work page 2015

  3. [3]

    Dorschner J., Begemann B., Henning T., Jaeger C., Mutschke H., 1995, , 300, 503

    work page 1995

  4. [4]

    T., 2003, , 41, 241

    Draine B. T., 2003, , 41, 241

    work page 2003

  5. [5]

    Draine B. T. et al. , 2014, , 780, 172

    work page 2014

  6. [6]

    T., Lee H

    Draine B. T., Lee H. M., 1984, , 285, 89

    work page 1984

  7. [7]

    T., Li A., 2007, , 657, 810

    Draine B. T., Li A., 2007, , 657, 810

    work page 2007

  8. [8]

    Dunne L., Eales S., Ivison R., Morgan H., Edmunds M., 2003, , 424, 285

    work page 2003

Show all 50 references
  1. [9]

    Fabian D., Henning T., J \"a ger C., Mutschke H., Dorschner J., Wehrhan O., 2001, , 378, 228

    2001

  2. [10]

    Fritz J. et al. , 2012, , 546, A34

    2012

  3. [11]

    Gordon K. D. et al. , 2014, , 797, 85

    2014

  4. [12]

    Griffin M. J. et al. , 2010, , 518, L3

    2010

  5. [13]

    Groves B. et al. , 2012, , 426, 892

    2012

  6. [14]

    S., Brooke T

    Hanner M. S., Brooke T. Y., Tokunaga A. T., 1998, , 502, 871

    1998

  7. [15]

    Henning T., Begemann B., Mutschke H., Dorschner J., 1995, , 112, 143

    1995

  8. [16]

    Henning T., Stognienko R., 1996, , 311, 291

    1996

  9. [17]

    Jaeger C., Dorschner J., Mutschke H., Posch T., Henning T., 2003, , 408, 193

    2003

  10. [18]

    J., Dorschner J., Henning T., Mutschke H., Waters L

    Jaeger C., Molster F. J., Dorschner J., Henning T., Mutschke H., Waters L. B. F. M., 1998, , 339, 904

    1998

  11. [19]

    Jaeger C., Mutschke H., Begemann B., Dorschner J., Henning T., 1994, , 292, 641

    1994

  12. [20]

    P., 2012, , 540, A2

    Jones A. P., 2012, , 540, A2

    2012

  13. [21]

    P., Fanciullo L., K \"o hler M., Verstraete L., Guillet V., Bocchio M., Ysard N., 2013, , 558, A62

    Jones A. P., Fanciullo L., K \"o hler M., Verstraete L., Guillet V., Bocchio M., Ysard N., 2013, , 558, A62

    2013

  14. [22]

    Kirkpatrick A. et al. , 2014, , 789, 130

    2014

  15. [23]

    K \"o hler M., Jones A., Ysard N., 2014, , 565, L9

    2014

  16. [24]

    T., 1993, , 402, 441

    Laor A., Draine B. T., 1993, , 402, 441

    1993

  17. [25]

    Lewis A. R. et al. , 2015, , 805, 183

    2015

  18. [26]

    T., 2001, , 554, 778

    Li A., Draine B. T., 2001, , 554, 778

    2001

  19. [27]

    A., Whitworth A

    Marsh K. A., Whitworth A. P., Lomax O., 2015, , 454, 4282

    2015

  20. [28]

    A., Whitworth A

    Marsh K. A., Whitworth A. P., Smith M. W. L., Lomax O., Eales S. A., 2018, , 480, 3052

    2018

  21. [29]

    S., 1990, , 28, 37

    Mathis J. S., 1990, , 28, 37

    1990

  22. [30]

    L., Edmunds M

    Morgan H. L., Edmunds M. G., 2003, , 343, 427

    2003

  23. [31]

    S., 1992, , 261, 567

    Ossenkopf V., Henning T., Mathis J. S., 1992, , 261, 567

    1992

  24. [32]

    Padoan P., Nordlund ., 2002, , 576, 870

    2002

  25. [33]

    Pegourie B., 1988, , 194, 335

    1988

  26. [34]

    Pilbratt G. L. et al. , 2010, , 518, L1

    2010

  27. [35]

    , 2014, , 564, A45

    Planck Collaboration et al. , 2014, , 564, A45

    2014

  28. [36]

    , 2015, , 582, A28

    Planck Collaboration et al. , 2015, , 582, A28

    2015

  29. [37]

    , 2016, , 596, A109

    Planck Collaboration et al. , 2016, , 596, A109

    2016

  30. [38]

    Poglitsch A. et al. , 2010, , 518, L2

    2010

  31. [39]

    Posch T., Kerschbaum F., Fabian D., Mutschke H., Dorschner J., Tamanai A., Henning T., 2003, , 149, 437

    2003

  32. [40]

    M., Corsi C

    Rich R. M., Corsi C. E., Cacciari C., Federici L., Fusi Pecci F., Djorgovski S. G., Freedman W. L., 2005, , 129, 2670

    2005

  33. [41]

    M., Marsh K

    Richardson J. M., Marsh K. A., 1991, in Maximum Entropy and Bayesian Methods, Smith C. R., Erickson G., Neudorfer P. O., eds., Springer, p. 213

    1991

  34. [42]

    G., 1991, , 377, 526

    Rouleau F., Martin P. G., 1991, , 377, 526

    1991

  35. [43]

    Saftly W., Baes M., De Geyter G., Camps P., Renaud F., Guedes J., De Looze I., 2015, , 576, A31

    2015

  36. [44]

    Schneider N. et al. , 2015 a , , 453, L41

    2015

  37. [45]

    Schneider N. et al. , 2015 b , , 575, A79

    2015

  38. [46]

    Smith M. W. L. et al. , 2012, , 756, 40

    2012

  39. [47]

    Tabatabaei F. S. et al. , 2014, , 561, A95

    2014

  40. [48]

    Williams B. F. et al. , 2014, , 215, 9

    2014

  41. [49]

    G., Mennella V., Colangeli L., Bussoletti E., 1996, , 282, 1321

    Zubko V. G., Mennella V., Colangeli L., Bussoletti E., 1996, , 282, 1321

    1996

  42. [50]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.