(csc). h Γ x-ray scattering from intergalactic dust h 0 x ...lia/poster_aas2011.pdfif no trace of...

If no trace of intergalactic dust is found, it must be locked up or destroyed in the halos of galaxies. Either result would provide new insight for dust evolution on the cosmic scale.

X-ray Scattering from Intergalactic Dust

Lia Corrales and Frits PaerelsColumbia University

[email protected]

By estimating the total mass of metals produced throughstar formation versus the amount of metals locked up in galax-ies and intergalactic gas, researchers have concluded thatabout half of the metals in the intergalactic medium are lockedup in dust grains, with ΩIGM

dust ∼ 10−5 [1].Large dust grains aremore likely to survive the processes, such as wind and radi-ation pressure, that enrich the intergalactic medium. Thusintergalactic dust is likely to be gray, leaving little trace ofoptical reddening that is typical of interstellar dust. We ex-plore the possibility of detecting large (∼ 1µm) intergalacticdust grains through small angle X-ray scattering. A brightX-ray point source, when imaged, will appear surrounded bya halo 10-100 arcseconds wide. The scattering cross sectionfor X-rays increases as a

4, where a is the grain radius. Fora power law distribution of grain sizes, the optical depth ofthe universe to soft X-ray scattering reaches 20% for sourcesout to z = 2. We present models of X-ray halos with variousgrain size distributions and explore the limits a dust-suffuseduniverse places on current and future X-ray missions, the de-termination of cosmological parameters, and intergalactic en-richment models.

1. Cosmological Halo Model

Models that weigh the competing forces of gravity, ra-diation pressure, and gas drag have shown that dust grains∼ 0.1 µm or more can easily be expelled from the disk of agalaxy, at least to a few kpc [2,3]. Some models have sug-gested that some dust survives well enough to enrich the halogas and the surrounding intergalactic medium [4,5]. Dustinhabiting the surrounding medium of galaxies has been ob-served by polarized, scattered light [6] and quasar reddeningalong lines of sight in the vicinity of foreground galaxies [7].

Dust in the IGM may not leave a clear trace of redden-ing because (i) small grains (a ≤ 0.1 µm) are preferentiallydestroyed via sputtering in a galaxy’s hot halo gas (Aguirre1999); and (ii) large grains, or grains with relatively flat opac-ities across optical wavelengths, are efficiently removed fromthe disks of galaxies via radiation pressure [2,3,5]. Thus, Iassume that the IGM contains dust grain sizes greater than0.1 µm at a constant co-moving density of Ωd = 10−5. Thiscan be considered an upper limit for situations z ∼> 2.5, be-cause the total metallically of the universe (and thus the totaldensity of dust) is smaller by a factor of ten in those cases.

1.1. Halo Integral

Figure 1 describes the path scattered light takes when itis emitted by a source at zs, interacts with a spherical grainof radius a at some intermediate redshift z, scatters onto a

α

– 8 –

show the individual halo profiles for several energies between 0.5 and 2.0 KeV for a

distribution of dust grains with 0.1 < a < 1.0 µm and p = 1.8. The black curve

shows the result of integrating the color curves using Γ = 2. The dashed line shows

the background count rates (counts per pixel) reported by the Chandra Source Catalog

(CSC).1

Fig. 4.— Caption for fig:qso1508

x =

zs

z

cdz

H(z)zs

0cdz

H(z)

3. Future Implications

REFERENCES

Aguirre, A. 1999, ApJ, 525, 583

Comastri, A., Setti, G., Zamorani, G., Elvis, M., Wilkes, B. J., McDowell, J. C., &

Giommi, P. 1992, ApJ, 384, 62

1http://cxc.harvard.edu/csc/

– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 9 –

0


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62

Inoue, A. K., & Kamaya, H. 2003, MNRAS, 341, L7

Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425

Mauche, C. W., & Gorenstein, P. 1986, ApJ, 302, 371

Menard, B., Scranton, R., Fukugita, M., & Richards, G. 2010, MNRAS, 405, 1025

Smith, R. K., & Dwek, E. 1998, ApJ, 503, 831

Weingartner, J. C., & Draine, B. T. 2001, ApJ, 548, 296

Wilkes, B. J., & Elvis, M. 1987, ApJ, 323, 243

Williams, O. R., et al. 1992, ApJ, 389, 157

This preprint was prepared with the AAS LATEX macros v5.2.

Fig. 1.— Geometry of scattered light from a cosmologicalsource (Equation 1).

small angle θscat, and is observed at the angular distance αfrom the center of the point source. The value x is used toparameterize the distance between the source and the grainscattering site. The intensity of the scattered X-ray light, fora single grain size and photon energy, is

Iscatν (α) = F

srcν

zs

0n0

(1 + z)2

x2

dσ(θscat)

dΩ

cdz

H(z)(1)

where the differential cross-section must be evaluated at thescattering angle θscat = α(1 + z)/x. F src

ν is the source flux asobserved at z = 0, and n0 is the constant co-moving numberdensity of dust grains. A flat ΛCDM cosmology is assumedso that H(z) = H0

Ωm(1 + z)3 + ΩΛ, with Ωm = 0.3 and

ΩΛ = 0.7.

1.2. Dust and Energy Distributions

Equation 1 can be integrated over a distribution of grainsizes and a spectral energy distribution. Since the currentknown mechanisms for IGM enrichment involve the expulsionof material from galaxies, I will start with known interstellardust distributions. The canonical paper by [8] showed that apower law distribution (n ∝ a

−p, with p ∼ 3.5) of graphiteand silicate grains could fit interstellar extinction curves. Amore recent result by [9], hereafter WD01, used a more com-plicated distribution whose parameters change according tothe observed RV (extinction to reddening coefficient). Mostof the parameters used by WD01 affect the shape of the distri-bution for very small grains (∼< 100 A). For grain sizes largerthan 0.1 µm, the WD01 parameters can be reduced to a powerlaw with the average p ≈ 1.8. The maximum grain size for agraphite WD01 distribution ranges from 0.6 to 2 µm. A sim-ple power-law will overestimate the number of largest grainsso it is cut off at 1 µm to balance the easy expulsion of largedust grains via radiation pressure with the existence, but se-vere drop in number, of ISM dust grains > 1 µm predicted byWD01.

Quasars provide an opportunity to observe X-ray halosbecause they appear as point sources, are often X-ray bright,and exist at distances large enough to experience a substantialoptical depth to soft X-ray scattering. The spectral energydistribution of many quasars are observed to follow a power-

– 4 –

Table 1: R50 (arcminutes) as a function of redshift and energy.

Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.353.0 KeV 0.16 0.11 0.08 0.06

3. Discussion

The optical depth for X-ray scattering increases promptly beyond redshift 1, but suffers from dimin-ishing returns beyond a redshift of 2 (see Figure 2). The most distant quasars also appear dimmer. Thebrightest quasar at z = 4, QSO 1508+5714 has a count rate ∼ 0.04 counts/sec. No halo was discoveredaround it suggesting that, if the universe does contain a uniform distribution of intergalactic dust, it musthave a density Ω ∼< 10−6 [15]. The assumption of uniformly distributed dust also may not hold until afterthe epoch of star formation, around z ∼ 2− 3. It is worthwhile to examine brighter quasars around z ∼ 2to further characterize the density of intergalactic dust. Observations of dust well outside the disk of agalaxy, and the availability of enrichment mechanisms, suggest that, if no trace of intergalactic dust isfound, it must be locked up or destroyed in the halos of galaxies. Either result would provide new insightfor dust evolution on the cosmic scale.

blaThe source flux asobserved at z = 0

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583

[2] Davies, J. I., Alton, P., Bianchi, S., & Trewhella, M. 1998, MNRAS, 300, 1006

[3] Murray, N., Quataert, E., & Thompson, T. A. 2005, ApJ, 618, 569

[4] Greenberg, J. M., Ferrini, F., Barsella, B., & Aiello, S. 1987, Nature, 327, 214

[5] Ferrara, A., Ferrini, F., Barsella, B., & Franco, J. 1991, ApJ, 381, 137

[6] Schmidt, G. D., Angel, J. R. P., & Cromwell, R. H. 1976, ApJ, 206, 888

[7] Menard, B., Scranton, R., Fukugita, M., & Richards, G. 2010, MNRAS, 405, 1025

[8] Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425

[9] Weingartner, J. C., & Draine, B. T. 2001, ApJ, 548, 296

[10] Comastri, A., Setti, G., Zamorani, G., Elvis, M., Wilkes, B. J., McDowell, J. C., & Giommi, P. 1992,ApJ, 384, 62

[11] Wilkes, B. J., & Elvis, M. 1987, ApJ, 323, 243

– 4 –


Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.353.0 KeV 0.16 0.11 0.08 0.06

3. Discussion



The constant co-movingnumber density of dust grains

A factor that modifiesthe source flux

Flat ΛCDM cosmology is assumed

H(z) = H0

Ωm(1 + z)3 + ΩΛ

with Ωm = 0.3 and ΩΛ = 0.7

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583







– 4 –


Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.353.0 KeV 0.16 0.11 0.08 0.06

3. Discussion




A factor that modifiesthe source flux

Flat ΛCDM cosmology is assumed

H(z) = H0

Ωm(1 + z)3 + ΩΛ

with Ωm = 0.3 and ΩΛ = 0.7

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583







Abstract



[email protected]

By estimating the total mass of metals produced through star formation versus the amount of metalslocked up in galaxies and intergalactic gas, researchers have concluded that about half of the metals in theintergalactic medium are locked up in dust grains, with ΩIGM

dust ∼ 10−5 [1].Large dust grains are more likelyto survive the processes, such as wind and radiation pressure, that enrich the intergalactic medium. Thusintergalactic dust is likely to be gray, leaving little trace of optical reddening that is typical of interstellardust. We explore the possibility of detecting large (∼ 1µm) intergalactic dust grains through small angleX-ray scattering. A bright X-ray point source, when imaged, will appear surrounded by a halo 10-100arcseconds wide. The scattering cross section for X-rays increases as a4, where a is the grain radius. Fora power law distribution of grain sizes, the optical depth of the universe to soft X-ray scattering reaches20% for sources out to z = 2. We present models of X-ray halos and explore the limits a dust-suffuseduniverse places on X-ray missions and intergalactic enrichment models.


Models that weigh the competing forces of gravity, radiation pressure, and gas drag have shown thatdust grains ∼ 0.1 µm or more can easily be expelled from the disk of a galaxy, at least to a few kpc[2,3]. Some models have suggested that some dust survives well enough to enrich the halo gas and thesurrounding intergalactic medium [4,5]. Dust inhabiting the surrounding medium of galaxies has beenobserved by polarized, scattered light [6] and quasar reddening along lines of sight in the vicinity offoreground galaxies [7].

Dust in the IGM may not leave a clear trace of reddening because (i) small grains (a ≤ 0.1 µm) arepreferentially destroyed via sputtering in a galaxy’s hot halo gas (Aguirre 1999); and (ii) large grains, orgrains with relatively flat opacities across optical wavelengths, are efficiently removed from the disks ofgalaxies via radiation pressure [2,3,5]. Thus, I assume that the IGM contains dust grain sizes greater than0.1 µm at a constant co-moving density of Ωd = 10−5. This can be considered an upper limit for situationsz ∼> 2.5, because the total metallically of the universe (and thus the total density of dust) is smaller by afactor of ten in those cases.

1.1. Halo Integral

Figure 1 describes the path scattered light takes when it is emitted by a source at zs, interacts with aspherical grain of radius a at some intermediate redshift z, scatters onto a small angle θscat, and is observedat the angular distance α from the center of the point source. The value x is used to parameterize thedistance between the source and the grain scattering site. The intensity of the scattered X-ray light, for asingle grain size and photon energy, is

Iscatν (α) = F

srcν

zs

0

n0(1 + z)2

x2

dσ(θscat)

dΩ

cdz

H(z)(1)

where the differential cross-section must be evaluated at the scattering angle θscat = α(1 + z)/x. Fsrcν is

the source flux as observed at z = 0, and n0 is the constant co-moving number density of dust grains. Aflat ΛCDM cosmology is assumed so that H(z) = H0

Ωm(1 + z)3 + ΩΛ, with Ωm = 0.3 and ΩΛ = 0.7.

L. R. Corrales (Columbia University), Frits Paerels (Columbia University)


α

– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 9 –

0


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62










– 2 –

α

– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 9 –

0


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62










Fig. 1.— The path scattered light takes when it is emitted by a source at zs, interacts with a sphericalgrain of radius a at some intermediate redshift z, scatters onto a small angle θscat, and is observed at theangular distance α from the center of the point source. The value x is used to parameterize the distancebetween the source and the grain scattering site.


Equation 1 can be integrated over a distribution of grain sizes and a spectral energy distribution.Since the current known mechanisms for IGM enrichment involve the expulsion of material from galaxies,I will start with known interstellar dust distributions. A power law distribution (n ∝ a−p, with p ∼ 3.5)of graphite and silicate grains can fit many interstellar extinction curves [8]. A more recent result ([9]),hereafter WD01, used a more complicated distribution whose parameters affect the shape of the distributionfor very small grains (∼< 100 A). For grain sizes larger than 0.1 µm, the WD01 parameters can be reducedto a power law with the median p ≈ 1.8. The maximum grain size for a graphite WD01 distributionranges from 0.6 to 2 µm. A simple power-law will overestimate the number of largest grains so it is cut offat 1 µm to balance the easy expulsion of large dust grains via radiation pressure with the existence, butsevere drop in number, of ISM dust grains > 1 µm predicted by WD01.

Quasars provide an opportunity to observe X-ray halos because they appear as point sources, are oftenX-ray bright, and exist at distances large enough to experience a substantial optical depth to soft X-rayscattering. The spectral energy distribution of many quasars are observed to follow a power-law such thatthe number of photons dN/dE ∝ E−Γ. Typical values of Γ are around 1.5 - 2.0 [10,11,12]. Quasars thatexhibit an excess of soft X-ray light would be ideal candidates for the study of X-ray halos, so I will useΓ = 2 as a canonical value.

2. Results

The Rayleigh-Gans approximation for X-ray scattering through small grains [13,14], leads to a scat-tering cross-section that is σscat ∝ E−2a4. I assume a constant co-moving number density and n(a) ∝ a−1.8.Figure 2 shows the optical depth of the universe for different soft X-ray photon energies: 0.5 KeV (black)and 1.0 KeV (blue). The solid lines depict the grain sizes 0.1 µm ≤ a ≤ 0.25, and the dashed lines depictthe grain sizes 0.1 µm ≤ a ≤ 1.0 µm.

Figure 3 shows the total integrated X-ray halo in the 0.5-2.0 KeV band, using a spectral energydistribution with photon index Γ = 2, and assuming a source luminosity of 0.1 counts/sec integrated over10 ks (red line). The pixel values reflect the specifications of Chandra, where one pixel ≈ 0.5 arcsecondswide. The grey lines show the halo for individual photon energies. The dashed line shows the typicalbackground count-rate for a back illuminated chip on the Chandra ACIS camera, integrated over 10 ks.The halo image is 13.5% of the source brightness.

Halo Intensity(Theory)

Application

Cosmological Models

Motivation

– 3 –

Fig. 2.— The optical depth of the universe for X-ray scattering of 0.5 KeV and 1.0 KeV photons. The

number density of dust grains is assumed such that n(a) ∝ a−1.8. The solid lines depict the grain sizes

0.1 µm ≤ a ≤ 0.25, and the dashed lines depict the grain sizes 0.1 µm ≤ a ≤ 1.0 µm.

Fig. 3.— The expected number of counts per pixel for scattered X-rays from a quasar at z=4, using a

total of 1000 source counts. The red line shows the halo image integrated over 0.5-2.0 KeV. The dashed

line indicates the typical background count-rate.

The halo image produced by scattered X-rays becomes more compact with larger redshift. Table 1

shows the radius containing 50% of the total halo light (R50) as it changes with redshift. This is because

the characteristic scattering angle decreases with increasing energy. For a fixed observed energy, photons

from a high redshift object scattered at a higher energy than photons from a low redshift object.

3. Discussion

The optical depth for X-ray scattering increases promptly beyond redshift 1, but the search for a halo

image suffers from diminishing returns beyond a redshift of 2 (Figure 2). The most distant quasars also

appear dimmer. The brightest quasar at z = 4, QSO 1508+5714 has a count rate ∼ 0.04 counts/sec.

No halo was discovered around it, suggesting that, if the universe does contain a uniform distribution of

1.0 µm intergalactic dust, it must have density Ω < 2 × 10−6 [15]. For a smaller populations of grains

(0.1 µm), the limit would be higher. The assumption of uniformly distributed dust also may not hold

The optical depth of the universe for X-ray scattering. In general --

– 4 –

Fig. 3.— The expected number of counts per pixel for scattered X-rays from a quasar at z=4, assuming asource luminosity of 0.1 counts/sec (for a total of 1000 source counts) in the 0.5 - 2.0 KeV band. The greylines show what the halo would be for fixed photon energies. The red line shows the halo image integratedusing Γ = 2. The dashed line indicates the typical background count-rate for a back illuminated chip onthe Chandra ACIS camera, integrated over 10 ks.

n(a) ∝ a−p with p = 1.8

τ ∝ ΩIGMdust a4−p E−2

σ ∝ a4E−2

dσ

dΩ=

2a2

9

2πa

λ

4

|m− 1|2 exp

−θ2scat

2∼σ2

∼σ =

1.04 arcmin

E(KeV) a(µm)

θscat =α(1 + z)

x

– 4 –


Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.35

3.0 KeV 0.16 0.11 0.08 0.06

of a galaxy, and the availability of enrichment mechanisms, suggest that, if no trace of intergalactic dust is

found, it must be locked up or destroyed in the halos of galaxies. Either result would provide new insight

for dust evolution on the cosmic scale.

blablabla

n0 ∝ ΩIGMdust

n(a) ∝ a−pwith p = 1.8


σ ∝ a4E−2

dσ

dΩ=

2a2

9

2πa

λ

4

|m− 1|2 exp

−θ2scat

2∼σ2

∼σ =

1.04 arcmin

E(KeV) a(µm)

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583









[10] Comastri, A., Setti, G., Zamorani, G., Elvis, M., Wilkes, B. J., McDowell, J. C., & Giommi, P. 1992,

ApJ, 384, 62


– 4 –


Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.35

3.0 KeV 0.16 0.11 0.08 0.06




blablabla

n0 ∝ ΩIGMdust



σ ∝ a4E−2

dσ

dΩ=

2a2

9

2πa

λ

4

|m− 1|2 exp

−θ2scat

2∼σ2

∼σ =

1.04 arcmin

E(KeV) a(µm)

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583










ApJ, 384, 62


– 4 –


Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.35

3.0 KeV 0.16 0.11 0.08 0.06




blablabla

n0 ∝ ΩIGMdust



σ ∝ a4E−2

dσ

dΩ=

2a2

9

2πa

λ

4

|m− 1|2 exp

−θ2scat

2∼σ2

∼σ =

1.04 arcmin

E(KeV) a(µm)

θscat =α(1 + z)

x

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583










ApJ, 384, 62

Gaussian approximation to the Rayleigh-Gans scattering cross-section [11]

with the standard deviation

– 4 –


n(a) ∝ a−p with p = 1.8


σ ∝ a4E−2

dσ

dΩ=

2a2

9

2πa

λ

4

|m− 1|2 exp

−θ2scat

2∼σ2

∼σ =

1.04 arcmin

E(KeV) a(µm)

θscat =α(1 + z)

x

To be observed:

and total cross-section

– 3 –




The halo image produced by scattered X-rays becomes more compact with larger redshift. Table ??shows the radius containing 50% of the total halo light (R50) as it changes with redshift. This is because



Table 1: The radius (in arcminutes) containing 50% of the total scattered light as it changes with redshiftand energy.

Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.35

3.0 KeV 0.16 0.11 0.08 0.06

3. Discussion


image suffers from diminishing returns beyond a redshift of 2 (Figure ??). The most distant quasars also





until after the epoch of star formation, z ∼ 2 − 3. It is worthwhile to examine brighter quasars around

z = 2 to further characterize the density of intergalactic dust. Observations of dust well outside the disk




blablabla

n0 ∝ ΩIGMdust

The radius (in arcminutes) containing 50% of the total scattered light as it changes with redshift and energy.

Halo images are more compact for a source at higher redshift

For a fixed observed energy, photons from a high-z source scattered at a higher energy (due to cosmological redshift) than photons from a low-z object.

– 4 –


n(a) ∝ a−p with p = 1.8


σ ∝ a4E−2

dσ

dΩ=

2a2

9

2πa

λ

4

|m− 1|2 exp

−θ2scat

2∼σ2

∼σ =

1.04 arcmin

E(KeV) a(µm)

θscat =α(1 + z)

x



[email protected]


dust ∼ 10−5 [1].Large dust grains aremore likely to survive the processes, such as wind and radi-ation pressure, that enrich the intergalactic medium. Thusintergalactic dust is likely to be gray, leaving little trace ofoptical reddening that is typical of interstellar dust. We ex-plore the possibility of detecting large (∼ 1µm) intergalacticdust grains through small angle X-ray scattering. A brightX-ray point source, when imaged, will appear surrounded bya halo 10-100 arcseconds wide. The scattering cross sectionfor X-rays increases as a4, where a is the grain radius. For apower law distribution of grain sizes, the optical depth of theuniverse to soft X-ray scattering reaches 20% for sources outto z = 2. We present models of X-ray halos and explore thelimits a dust-suffused universe places on X-ray missions andintergalactic enrichment models.


Models that weigh the competing forces of gravity, ra-diation pressure, and gas drag have shown that dust grains∼ 0.1 µm or more can easily be expelled from the disk of agalaxy, at least to a few kpc [2,3]. Dust outside the plane ofthe galaxy can be found by examining polarized light, whichhas scattered off dust grains several kpc from the disk of M82[4]. Graphite grains larger than 0.1 µm can survive hot gastemperatures to enrich the halo gas and perhaps the surround-ing intergalactic medium [5,6]. A study that found correlationbetween quasar color and angular distance from the center offoreground galaxies implied that dust enriches regions fromabout 20 kpc to 1 Mpc scales [7].

Dust in the IGM may not leave a clear trace of redden-ing because (i) small grains (a ≤ 0.1 µm) are preferentiallydestroyed via sputtering in hot halo gas [1]; and (ii) largegrains, or grains with relatively flat opacities across opticalwavelengths, are efficiently removed from the disks of galax-ies [2,3,5]. For now I assume that the IGM contains dust grainsizes greater than 0.1 µm at a constant co-moving density ofΩd = 10−5.

1.1. Halo Integral

Figure 1 describes the path scattered light takes when itis emitted by a source at zs, interacts with a spherical grainof radius a at some intermediate redshift z, scatters onto asmall angle θscat, and is observed at the angular distance αfrom the center of the point source. The value x is used to

α

– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 9 –

0


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62











parameterize the distance between the source and the grainscattering site. The intensity of the scattered X-ray light, fora single grain size and photon energy, is

Iscatν (α) = F

srcν

zs

0n0

(1 + z)2

x2

dσ(θscat)

dΩ

cdz

H(z)(1)




ΩΛ = 0.7.


Equation 1 can be integrated over a distribution of grainsizes and a spectral energy distribution. Since the currentknown mechanisms for IGM enrichment involve the expulsionof material from galaxies, I will start with known interstellardust distributions. A power law distribution (n ∝ a

−p, withp ∼ 3.5) of graphite and silicate grains can fit many interstel-lar extinction curves [8]. A more recent result ([9]), hereafterWD01, used a more complicated distribution whose parame-ters affect the shape of the distribution for very small grains(∼< 100 A). For grain sizes larger than 0.1 µm, the WD01parameters can be reduced to a power law with the medianp ≈ 1.8.

Quasars provide an opportunity to observe X-ray halosbecause they appear as point sources, are often X-ray bright,and exist at distances large enough to experience a substantialoptical depth to soft X-ray scattering. The spectral energydistribution of many quasars are observed to follow a power-law such that the number of photons dN/dE ∝ E

−Γ. Typicalvalues of Γ are around 1.5 - 2.0 [e.g. 10]. Quasars that exhibitan excess of soft X-ray light would be ideal candidates for thestudy of X-ray halos, so I will use Γ = 2 as a canonical value.

2. Results

The Rayleigh-Gans approximation for X-ray scatteringthrough small grains [13,14], leads to a scattering cross-sectionthat is σscat ∝ E

−2a4. I assume a constant co-moving number

An X-ray Halo Integrated for a Model Quasar

A halo image integrated for a model quasar whose brightness yields 1000 photon counts between 0.5 and 2.0 KeV.

Total number ofscattered photons

Total number ofsource photons= 13.5 % of

1 pixel = 0.5” (Chandra imaging)

Soft X-rayBackground

– 2 –

Fig. 2.— Optical depth of the universe for X-ray scattering

of 0.5 KeV and 1.0 KeV photons.

Fig. 3.— The expected number of counts per pixel for scat-

tered X-rays from a quasar at z=4, using a total of 1000 source

counts. The red line shows the halo image integrated over 0.5-

2.0 KeV. The dashed line indicates the typical background

count-rate.

KeV (black) and 1.0 KeV (blue). The solid lines depict the

grain sizes 0.1 µm ≤ a ≤ 0.25, and the dashed lines depict

the grain sizes 0.1 µm ≤ a ≤ 1.0 µm.

Figure 3 shows the total integrated X-ray halo in the

0.5-2.0 KeV band, using a spectral energy distribution with

photon index Γ = 2, and assuming a source luminosity of 0.1

counts/sec integrated over 10 ks (red line). The pixel values

reflect the specifications of Chandra, where one pixel ≈ 0.5arcseconds wide. The grey lines show the halo for individ-

ual photon energies. The dashed line shows the typical back-

ground count-rate for a back illuminated chip on the Chandra

ACIS camera, integrated over 10 ks. The halo image is 13.5%

of the source brightness.

The halo image produced by scattered X-rays becomes

more compact with larger redshift. Table 1 shows the radius

containing 50% of the total halo light (R50) as it changes

with redshift. This is because the characteristic scattering

angle decreases with increasing energy. For a fixed observed

energy, photons from a high-z source scattered at a higher

energy than photons from a low-z source.


Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.35

3.0 KeV 0.16 0.11 0.08 0.06

3. Discussion

blablabla

• The wings of the Chandra PSF need to be well-

characterized. Chandra provides sufficient resolution

(0.5” per pixel) to detect halo images ∼ 30”. Distin-

guishing a dim halo image from the wings of a PSF will

be at the forefront of the continuing project.

• The optical depth for X-ray scattering increases promptly

beyond redshift 1, but the search for a halo image

suffers from diminishing returns beyond a red-

shift of 2 (Figure 2).

• The most distant quasars also appear dimmer.

The brightest quasar at z = 4, QSO 1508+5714 has a

count rate ∼ 0.04 counts/sec. No halo was discovered

around it, suggesting that, if the universe does contain a

uniform distribution of 1.0 µm intergalactic dust, it must

have density Ω < 2×10−6 [12]. For a smaller populations

of grains (0.1 µm), the limit would be higher.

• The assumption of uniformly distributed dust

also may not hold until after the epoch of star

formation, z ∼ 2 − 3. It is worthwhile to examine

brighter quasars around z = 2 to further characterize the

density of intergalactic dust.

Observations of dust well outside the disk of a

galaxy, and the availability of enrichment

mechanisms, suggest that, if no trace of intergalactic

dust is found, it must be locked up or destroyed in

the halos of galaxies. Either result would provide

new insight for dust evolution on the cosmic scale.

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583

[2] Davies, J. I., Alton, P., Bianchi, S., & Trewhella, M. 1998,

MNRAS, 300, 1006

[3] Murray, N., Quataert, E., & Thompson, T. A. 2005, ApJ,

618, 569



[email protected]





Dust in the IGM may not leave a clear trace of reddeningbecause(i) small grains (a ≤ 0.1 µm) are preferentially de-

stroyed via sputtering in hot halo gas [1]; and(ii) large grains, or grains with relatively flat opacities

across optical wavelengths, are efficiently removed

from the disks of galaxies [2,3,5].

For now I assume that the IGM contains dust grain sizesgreater than 0.1 µm at a constant co-moving density of Ωd =10−5.

1.1. Halo Integral

Figure 1 describes the path scattered light takes when itis emitted by a source at zs, interacts with a spherical grain

α

– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 9 –

0


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62











of radius a at some intermediate redshift z, scatters onto asmall angle θscat, and is observed at the angular distance αfrom the center of the point source. The value x is used toparameterize the distance between the source and the grainscattering site. The intensity of the scattered X-ray light, fora single grain size and photon energy, is

Iscatν (α) = F

srcν

zs

0n0

(1 + z)2

x2

dσ(θscat)

dΩ

cdz

H(z)(1)




ΩΛ = 0.7.


Since the current known mechanisms for IGM enrichmentinvolve the expulsion of material from galaxies, I will startwith known interstellar dust distributions. A power law dis-tribution (n ∝ a

−p, with p ∼ 3.5) of graphite and silicategrains can fit many interstellar extinction curves [8]. A morerecent result ([9]), hereafter WD01, used a more complicateddistribution whose parameters affect the shape of the distri-bution for very small grains (∼< 100 A). For grain sizes largerthan 0.1 µm, the WD01 parameters can be approximated bya power law with the median p ≈ 1.8.



2. Results

The Rayleigh-Gans approximation for X-ray scatteringthrough small grains [11], leads to a scattering cross-section

– 5 –

REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583










ApJ, 384, 62

al. 1992, ApJ, 389, 157

[11] Mauche, C. W., & Gorenstein, P. 1986, ApJ, 302, 371

[12] Petric, A., Telis, G. A., Paerels, F., & Helfand, D. J. 2006, ApJ, 651, 41


– 4 –


Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.353.0 KeV 0.16 0.11 0.08 0.06

3. Discussion

The optical depth for X-ray scattering increases promptly beyond redshift 1, but suffers from dimin-ishing returns beyond a redshift of 2 (see Figure ??). The most distant quasars also appear dimmer. Thebrightest quasar at z = 4, QSO 1508+5714 has a count rate ∼ 0.04 counts/sec. No halo was discoveredaround it suggesting that, if the universe does contain a uniform distribution of intergalactic dust, it musthave a density Ω ∼< 10−6 [15]. The assumption of uniformly distributed dust also may not hold until afterthe epoch of star formation, around z ∼ 2− 3. It is worthwhile to examine brighter quasars around z ∼ 2to further characterize the density of intergalactic dust. Observations of dust well outside the disk of agalaxy, and the availability of enrichment mechanisms, suggest that, if no trace of intergalactic dust isfound, it must be locked up or destroyed in the halos of galaxies. Either result would provide new insightfor dust evolution on the cosmic scale.



REFERENCES

[1] Aguirre, A. 1999, ApJ, 525, 583









[10] Comastri, A., Setti, G., Zamorani, G., Elvis, M., Wilkes, B. J., McDowell, J. C., & Giommi, P. 1992,ApJ, 384, 62

– 3 –




The halo image produced by scattered X-rays becomes more compact with larger redshift. Table 1

shows the radius containing 50% of the total halo light (R50) as it changes with redshift. This is because



Table 1: The radius (in arcminutes) containing 50% of the total scattered light as it changes with redshiftand energy.

Energy z = 1 2 3 4

0.5 KeV 0.48 0.45 0.40 0.35

3.0 KeV 0.16 0.11 0.08 0.06

3. Discussion


image suffers from diminishing returns beyond a redshift of 2 (Figure 2). The most distant quasars also





until after the epoch of star formation, z ∼ 2 − 3. It is worthwhile to examine brighter quasars around

z = 2 to further characterize the density of intergalactic dust. Observations of dust well outside the disk




blablabla

n0 ∝ ΩIGMdust

Sensitivity to Dust Grain Size Limits



[email protected]





Dust in the IGM may not leave a clear trace of redden-ing because (i) small grains (a ≤ 0.1 µm) are preferentiallydestroyed via sputtering in hot halo gas [1]; and (ii) largegrains, or grains with relatively flat opacities across opticalwavelengths, are efficiently removed from the disks of galax-ies [2,3,5]. For now I assume that the IGM contains dust grainsizes greater than 0.1 µm at a constant co-moving density ofΩd = 10−5.

1.1. Halo Integral

Figure 1 describes the path scattered light takes when itis emitted by a source at zs, interacts with a spherical grainof radius a at some intermediate redshift z, scatters onto asmall angle θscat, and is observed at the angular distance αfrom the center of the point source. The value x is used to

α

– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 8 –





(CSC).1


x =

zs

z

cdz

H(z)zs

0cdz

H(z)

θscat

zs

z


– 9 –

0


REFERENCES

Aguirre, A. 1999, ApJ, 525, 583


Giommi, P. 1992, ApJ, 384, 62











parameterize the distance between the source and the grainscattering site. The intensity of the scattered X-ray light, fora single grain size and photon energy, is

Iscatν (α) = F

srcν

zs

0n0

(1 + z)2

x2

dσ(θscat)

dΩ

cdz

H(z)(1)




ΩΛ = 0.7.


Since the current known mechanisms for IGM enrichmentinvolve the expulsion of material from galaxies, I will startwith known interstellar dust distributions. A power law dis-tribution (n ∝ a

−p, with p ∼ 3.5) of graphite and silicategrains can fit many interstellar extinction curves [8]. A morerecent result ([9]), hereafter WD01, used a more complicateddistribution whose parameters affect the shape of the distri-bution for very small grains (∼< 100 A). For grain sizes largerthan 0.1 µm, the WD01 parameters can be approximated bya power law with the median p ≈ 1.8.



2. Results

The Rayleigh-Gans approximation for X-ray scatteringthrough small grains [11], leads to a scattering cross-sectionthat is σscat ∝ E

−2a4. I assume a constant co-moving number

density and n(a) ∝ a−1.8. Figure 2 shows the optical depth

of the universe for different soft X-ray photon energies: 0.5

(csc). h Γ x-ray scattering from intergalactic dust h 0 x ...lia/poster_aas2011.pdfif no trace of...

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