Upcoming surveys with the Herschel Space Observatory will yield far-IR
photometry of large samples of young stellar objects, which will require
careful interpretation. We investigate the color and luminosity diagnostics
based on Herschel broad-band filters to identify and discern the properties of
low-mass protostars. We compute a grid of 2,016 protostars in various physical
congurations, present the expected flux densities and flux density ratios for
this grid of protostars, and compare Herschel observations of three protostars
to the model results. These provide useful constraints on the range of colors
and fluxes of protostar in the Herschel filters. We find that Herschel data
alone is likely a useful diagnostic of the envelope properties of young starsComment: Part of HOPS KP papers to the Herschel special A&A issu

André

B. Ali

C. A. Poteet

Drain

E. Furlan

Fischer

Griffin

J. J. Tobin

L. Allen

L. Hartmann

M. Osorio

Menten

N. Calvet

Pilbratt

Poglitsch

Robitaille

S. T. Megeath

Tobin

W. J. Fischer

English

arXiv

Crossref

Astronomy and Astrophysics

Predicted colors and flux densities of protostars in the<i>Herschel</i>PACS and SPIRE filters

Upcoming surveys with the Herschel Space Observatory will yield far-IR photometry of large samples of young stellar objects, which will require careful interpretation. We investigate the color and luminosity diagnostics based on Herschel broad-band filters to identify and discern the properties of low-mass protostars. We compute a grid of 2016 protostars in various physical congurations, present the expected flux densities and flux density ratios for this grid of protostars, and compare Herschel observations of three protostars to the model results. These provide useful constraints on the range of colors and fluxes of protostar in the Herschel filters. We find that Herschel data alone is likely a useful diagnostic of the envelope properties of young stars

Ali, B.

Tobin, J. J.

Fischer, W. J.

Poteet, C. A.

Megeath, S. T.

Allen, L.

Hartmann, L.

Calvet, N.

Furlan, E.

Osorio, M.

Caltech Authors - Main

A&A 518, L119 (2010)
DOI: 10.1051/0004-6361/201014599
c© ESO 2010
Astronomy
&Astrophysics
Herschel: the first science highlights Special feature
Letter to the Editor
Predicted colors and flux densities of protostars in the Herschel
PACS and SPIRE filters
B. Ali1, J. J. Tobin2, W. J. Fischer3, C. A. Poteet3, S. T. Megeath3, L. Allen4, L. Hartmann2, N. Calvet2,
E. Furlan5 ,, and M. Osorio6
1 NHSC/IPAC, California Institute of Technology, Pasadena, CA USA
e-mail: babar@ipac.caltech.edu
2 University of Michigan, Ann Arbor, Michigan USA
3 University of Toledo, Toledo, OH USA
4 NOAO, Tucson, AZ USA
5 JPL, Caltech, Pasadena, CA, USA
6 Instituto de Astrofisica de Andalucia, Granada, Spain
Received 31 March 2010 / Accepted 27 April 2010
ABSTRACT
Upcoming surveys with the Herschel Space Observatory will yield far-IR photometry of large samples of young stellar objects, which
will require careful interpretation. We investigate the color and luminosity diagnostics based on Herschel broad-band filters to identify
and discern the properties of low-mass protostars. We compute a grid of 2016 protostars in various physical congurations, present the
expected flux densities and flux density ratios for this grid of protostars, and compare Herschel observations of three protostars to
the model results. These provide useful constraints on the range of colors and fluxes of protostar in the Herschel filters. We find that
Herschel data alone is likely a useful diagnostic of the envelope properties of young stars.
Key words. stars: protostars – radiative transfer – submillimeter: stars
1. Introduction
A comprehensive theory of star formation is necessary for un-
derstanding processes spanning the entire range of cosmic evo-
lution, from the formation and evolution of galaxies to the
formation of planets. Thus, observing the formation of stars
is one of the prime science objectives of the Herschel Space
Observatory Pilbrat et al. 2010. With its large (3.5 m) primary
mirror, Herschel is able to survey a substantial fraction of the
current star formation in the Galaxy with unprecedented eﬃ-
ciency and sensitivity. The result will be an explosion of far-IR
and sub-mm data on star formation regions. Herschel is partic-
ularly suited for carrying out these surveys because the spectral
energy distributions (SEDs) of protostars peaks in the far-IR and
sub-mm region. A large number of guaranteed- and open- time
key (legacy) Herschel programs are, thus, focused on star forma-
tion regions. These include PACS (Photodetector Array Camera
and Spectrometer, Poglitsch et al. 2010) and SPIRE (Spectral
and Imaging Reciever, Griﬃn et al. 2010) imaging surveys of
the Gould Belt (André et al. 2010), and the Herschel Orion
Protostar Survey (HOPS) and DIGIT programs, among others.
These surveys will detect hundreds of thousands of pro-
tostars. For our purposes, protostars are low-mass stars in
 Herschel is an ESA space observatory with science instruments
provided by Principal Investigator consortia. It is open for proposals
for observing time from the worldwide astronomical community.
 Spitzer Fellow.
the earliest stages of their evolution. They are less than a
few ×105 yrs old and are still surrounded by an infalling en-
velope. The SEDs of these protostars will be complex mixture
of their intrinsic emission coupled with reprocessing and emis-
sion from their immediate environment. Radiative transfer mod-
els are an important tool in understanding and interpretting the
observed flux densities of protostars. Model SEDs can provide
crucial constraints on the most important physical parameters
of a protostellar system. Because protostars can encompass a
wide rage of parameter space it is often necessary to compare
observations against a large number of diﬀerent models to de-
rive a reasonable solution and to understand the degeneracies
involved. Robitaille et al. (2006) constructed a grid of 20 000 in-
dividual models for SED fitting; however, these models used an
ism model for the envelope, which is not accurate at far-IR wave-
lengths. This is because reprocessing by dust is especially impor-
tant at Herschel’s wavelengths as this reprocessed light forms the
bulk of the protostars’ SED. In this contribution, we have gen-
erated a grid of 20 160 SEDs from 2016 individual protostar1
models focused primarily on the parameter space appropriate for
young stars, and for the Herschel broad-band filters.
2. The model grid and flux predictions
We use the Monte Carlo radiative transfer code developed
by Whitney et al. (2003), which is adapted to include the dust
1 There are 10 diﬀerent inclination angles for each of 2016 protostars.
Article published by EDP Sciences Page 1 of 4
A&A 518, L119 (2010)
mixture properties from Tobin et al.(2008) to calculate the model
SEDs. For convenience, we briefly summarize the main com-
ponents here. The code comprises four physical components:
(i) a central object; (ii) a flared disk; (iii) a rotating collapsing
envelope; and (iv) a bipolar cavity. These components are il-
lustrated in Fig. 1. The star+disk system emits energy packets
(“photons”) that are absorbed or scattered by the disk and/or en-
velope, subsequently determining the emergent SED of the sys-
tem. Our adopted dust model uses the methodology described
by D’Alessio et al. (2001) with additional optical constants for
graphite from Draine & Lee (1984). The dust grains used here
are a mixture of graphite, silicate and water ice and their number
density has a power-law distribution with grain size to the power
–3.5 and include large (1 micron radius) grains; the implied gas-
to-dust ratio is 133.
The code was used to produce a grid of 20 160 model SEDs
using 2 × 107 photons for the Monte Carlo computations, and
by using various configurations for the main components listed
above. We restricted the variable parameter set to: the infall rate
( ˙Menv), the maximum envelope size (Renv,max), the cavity open-
ing angle (θC), the cavity shape exponent (b), the accretion rate
( ˙Mdisk), the size of the disk (Rdisk,max), and the inclination an-
gle of the system to the observer’s line of sight (i). These are the
critical parameters that predominantly determine the flux density
prediction for Herschel PACS and SPIRE bands (56–610 μm).
The remaining parameters have fixed values that are typical for
low-mass protostars (Tobin et al. 2008).
One important characteristic of the code is that the disk ac-
cretion rate is used in the model grid to vary the luminosity of the
protostellar systems; the central star is fixed at 1 L. This is rea-
sonable since we do not know the relative contribution of pho-
tospheric and accretion luminosities in protostars. However, the
spectrum of the central object’s emission does not largely aﬀect
the emergent spectrum of the protostar in the far-IR since nearly
all emission is reprocessed. Thus, dust opacities are a more crit-
ical and relevant factor for our analysis.
Table 1 summarizes the relevant model parameters and
their values in our grid. We list only select parameters (see
Tobin et al. 2008 for a complete list). The properties of the cen-
tral object are perhaps the most crucial of the fixed parameters
in that changing the parameters for central object may lead to
degeneracies in the observed colors and fluxes. We discuss this
further in Sect. 3.5. Other relevant limitations of the model are
that dust opacities, which are known to vary across regions, are
assumed to be constant, and that only the water ice opacities for
the 3.6 μm feature are included in addition to dust.
2.1. Synthetic photometry
The code computes model SEDs for a given spatial extent (aper-
ture) of the system. We use aperture radius of 20 000 AU.
This collects the total integrated flux from the envelopes which
are all smaller than the aperture. We convolved the resulting
SEDs with the filter+detector transmission curves of PACS and
SPIRE (kindly provided by their respective instrument teams).
We present the results as flux density values at the central wave-
lengths of the filters. The model fluxes are calculated at the dis-
tance of Orion, adopted to be 420 pc (Menten et al. 2007).
3. Results and discussion
Figures 2−6 show the results for the 20 160 model SEDs calcu-
lated for our grid for various combinations of flux densities and
Mass Infall
Envelope
Disk
i
opening
angle
Rdisk,max
Cavity
Renv,max
Observ
line of 
Fig. 1. Illustration of some of the major parameters used to model the
protostar SEDs.
flux density ratios. The shaded dots shows the full range of pre-
dicted flux densities for the entire set of 2016 protostar systems
as seen with 10 diﬀerent inclination angles each. The parameter
values used here sample a broad range of physical conditions in
the protostars and, thus, provide a reasonable comparative range
of expected flux densities and flux density ratios for protostars.
In protostellar systems, model grids, such as the one
discussed here, are most accurate and useful when multi-
wavelength data are available to provide as many constraints as
possible (see e.g. Fischer et al. 2010). Nonetheless, PACS and
SPIRE sample the peak of the protostar’s SED and we expect
Herschel data alone to provide a relatively good estimate of the
envelope properties in particular.
We further investigate the eﬀect of each of the variable pa-
rameters on the observed fluxes. To illustrate how a particular
model parameter aﬀects the flux densities, we first selected a typ-
ical protostar system, here defined to have the following values:
˙Mdisk = 10−7 M yr−1, Rdisk,max = 100 AU, ˙Menv = 10−5 M yr−1,
Renv,max = 10 000 AU, θC = 25 degrees, b = 1.5, and i = 63.3 de-
grees. Then, we show how individual parameters aﬀect the re-
sults as they vary over the range listed in Table 1, while hold-
ing all other parameters constant. The results are color-coded (as
listed in the legend boxes in the upper left hand part of Figs. 2–6)
and shown as thick dashed lines. We show and discuss below re-
sults from a representative set of correlations investigated from
the full grid of model parameter range. We omit discussion on
˙Mdisk, as this parameter and its use in the code is already dis-
cussed above (see Sect. 2).
3.1. Envelope infall rate
The mass infall rate strongly aﬀects the far-IR flux and not sur-
prisingly, the predicted flux density and their ratios typically
vary by factors ∼2 as a function of ˙Menv. This is straight forward
as increasing the amount of infall simply increases the amount
of cold material and thus the far-IR fluxes. We expect to be able
to constrain the envelope infall rates with relatively good preci-
sion with Herschel data alone, although, some knowledge about
the distance to the source (or its luminosity) is required, or must
be assumed.
3.2. Envelope size
The size of the envelope directly aﬀects the amount of the cold-
est dust present in the protostar. Thus, we note significantly more
variation in the longer wavelength SPIRE filters (see Figs. 5–6)
Page 2 of 4
B. Ali et al.: Predicted colors and flux densities of protostars in the Herschel PACS and SPIRE filters
Table 1. Model parameters.
Parameter Description Value(s)
Central object & observer:
M∗(M) Mass of the central object. 0.5
R∗ (R) Radius of the central object. 2.09
T∗(K) Surface temperature of the central object. 4000
i (degrees) Inclination angle 18.2, 31.8, 41.4, 49.5, 56.7, 63.3, 69.5, 75.6, 81.4, 87.2
Envelope Properties:
˙Menv (×10−6 M yr−1) Mass infall rate 1, 5, 7.5, 10, 25, 50, 100
Renv,max (AU) Envelope outer radius 5000, 10 000, 15 000
Renv,min (R∗) Envelope inner radius 42.75
RC (AU) Centrifugal radius Equal to Rdisk,max
Disk properties:
Mdisk (M) Disk mass 0.05
˙Mdisk (×10−8 M yr−1) Disk accretion rate/Luminositya 1, 10, 100, 1000
Rdisk,max (AU) Disk outer radius 5, 100, 500
Rdisk,min Disk inner radius Set by dust destruction radius.
α disk radial density exponent 2.125
β disk scale height exponent 1.125
Cavity properties
θC (degrees) Cavity opening angle 5, 15, 25, 45
b Cavity shape exponent 1.5, 2.0
Notes. Parameters in bold are model grid variables. (a) See Sect. 2 for the coupling between ˙Mdisk and luminosity.
Fig. 2. Predicted results for the PACS 70 μm filter vs. the ratio of
70 to 160 μm flux density. The fluxes are reported for a protostar at
the distance of Orion. The shaded region shows the full range in the
20 160 SEDs in the grid. The color-coded (inset) thick dashed lines il-
lustrate the magnitude and direction of the parameter when all other pa-
rameters are held constant. We do this by choosing typical values (see
text) and plotting the variation from only one parameter for that proto-
star. The diamond symbols show the locations of the 3 HOPS protostars
(see Sect. 3.6).
than in the PACS filters. Increasing the outer radius of the en-
velope preferentially creates a comparatively redder protostellar
system. However, the aﬀect of the Renv,max is still appreciably
lower than ˙Menv. That’s because the latter more directly con-
trols the envelope density and total amount of emitting material
present in the envelope.
3.3. Cavity opening angle
The PACS fluxes appears to be most strongly aﬀected by this
parameter (see Figs. 2 and 4). This is likely because the width
of the cavity preferentially carves away the part of the envelope
Fig. 3. Same as Fig. 2 but this time for the 3 parameters that appear
to produce little or no eﬀect on the observed flux densities. This figure
is a magnified portion of the range of values shown in Fig. 2. The ef-
fect of these parameters will not be visible if shown over the full range
displayed in Fig. 2.
responsible for the 70 μm flux. By contrast, there is almost no
variation as a function of θC in the SPIRE filters.
3.4. Inclination angle
The optical and near-IR emission from protostellar systems is
dominated by the source itself and the scattered light from
the circumstellar envelope. Thus, face-on models are typically
brighter and bluer compared to those in which the central star
is either wholly or partially obscured by the disk. At optical
and near-IR wavelengths, these objects are quite often extremely
faint or undetected even in unbiased photometry surveys due to
high obscurataion. Figure 3 shows that in the PACS filters this
eﬀect becomes largely unimportant as the main emission is from
the envelope. We find similar results for the other combinations
of flux and flux density diagnostics (not shown).
Page 3 of 4
A&A 518, L119 (2010)
Fig. 4. The ratio of the PACS flux densities, 70 μm/100 μm vs.
100 μm/160 μm. The symbols and lines are as shown in Fig. 2.
Fig. 5. The SPIRE 250 μm flux density vs. the ratio 250 μm/350 μm.
The symbols and lines are as in Fig. 2.
Fig. 6. The PACS (70 μm/160 μm) ratio vs. the SPIRE (250 μm/350 μm)
ratio.
3.5. The central object
We have concentrated on a single central star; however, the
models are applicable to all low mass stars. The observed fluxes
and SEDs simply scale with the mass of the central object as
determined by the envelope density profile and the accretion lu-
minosity equations. When the mass of the central star is changed,
the envelope density remains the same but the infall rate changes.
And, the mass accretion rate for a given luminosity scales in-
versely with the central object mass. Thus, considerable overlap
does exist in the observed fluxes for diﬀerent mass protostars.
This result further demonstrates that PACS and SPIRE are best
suited for constraining the envelope and disk properties and pro-
vide limited constraints on the central object itself.
3.6. The HOPS protostars sample
The HOPS program (Fischer et al. 2010) imaged 4 protostars in
Orion L 1641 region for which PACS 70 and 160 μm photom-
etry is available for 3 sources. These stars are shown with the
diamond symbol in Fig. 2. Based on this diagnostic alone, we
can conclude that all 3 HOPS sources are much more luminous
than our typical protostar of 1 L. Only 3 sources with two-band
photometry are in the HOPS field; nonetheless, the sources are
not clustered but spread over a broad range of color and flux den-
sity values in Fig. 2, implying that a broad range of values must
also exist for the other parameters. These conclusions are indeed
confirmed by detailed model SED fits over the 1–870 μm range
for the HOPS sources (Fischer et al. 2010).
4. Conclusions
The model grid presented here provides the expected flux den-
sities and flux density ratios for 20 160 low-mass protostellar
SEDs, useful for determining the phase space occupied by pro-
tostar in the Herschel filters. Disentangling the contributions
of the various physical components that make up a protostel-
lar system is observationally challenging and requires multi-
wavelength data to properly constrain the properties of the sys-
tem. Nonetheless, preliminary results show that the fluxes in the
Herschel PACS and SPIRE filters are dominated by reprocessed
light and emission from the protostellar envelope. Herschel data
alone is, therefore, expected to be able to discern envelope prop-
erties with some precision provided that a reasonable estimate
for the object’s distance or its luminosity is available. The source
of the emission (combination of central star and disk accretion)
is relatively unimportant at Herschel far-IR and sub-mm wave-
lengths. Thus, Herschel data is unlikely to constrain the mass of
the central object, but sampling the peak of the protostars SED
allows tight constrains on its total luminosity.
Acknowledgements. We thank B. Whitney for making her code available pub-
licly. B. Ali acknowledges support from NASA grant IPAC.ALI-OTKP-1-
JPL.000094. J. J. Tobin acknowledges support from NASA grant HST-GO-
11548.04-A.
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Page 4 of 4


Predicted colors and flux densities of protostars in the Herschel PACS and SPIRE filters

Upcoming surveys with the Herschel Space Observatory will yield far-IR photometry of large samples of young stellar objects, which will require careful interpretation. We investigate the color and luminosity diagnostics based on Herschel broad-band filters to identify and discern the properties of low-mass protostars. We compute a grid of 2016 protostars in various physical congurations, present the expected flux densities and flux density ratios for this grid of protostars, and compare Herschel observations of three protostars to the model results. These provide useful constraints on the range of colors and fluxes of protostar in the Herschel filters. We find that Herschel data alone is likely a useful diagnostic of the envelope properties of young stars

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Predicted colors and flux densities of protostars in the

Predicted Colors and Flux Densities of Protostars in the Herschel PACS
  and SPIRE Filters

Predicted Colors and Flux Densities of Protostars in the Herschel PACS and SPIRE Filters

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