Marco Fatuzzo,Fred C. Adams, and Fulvio Melia 2006

1. CR enhancement in SNR/MC environments

2.How CR from SNR/MC influence ionization rate

3.How CR influence star formation

Previous works: Evidence for the hadronic process has been

found through the association of at least 10 EGRET sources with SNRs expanding into MCs.

The EGRET SNRs have inferred gamma-ray luminosities spanning Lr ∼ 1034 to 4x1036 erg s-

1(30 MeV–10 GeV). Particle acceleration in the SNR/MC environments

can significantly enhance the cosmic-ray (CR) density above that of the local background “sea” surrounding these regions (Aharonian & Atoyan 1996, hereafter AA96; Torres et al. 2003).

Diffusion of CR continues until they undergo p-p scattering with the ambient medium, and thereby experience catastrophic losses, on a timescale given by

Setting the τp-p equal to the diffusion timescale

estimate the distance R(E) that particles will diffuse into the cloud before scattering and losing their energy

Adopt energy-dependent diffusion coefficient from Ormes et al. 1988

The length scale is estimated to be

weakly dependent on energy for relativistic protons and is given by

(Mannheim & Schlickeiser 1994). corresponding cooling time

The cooling time is considerably longer than p-p collision

The resulting energy density uCR within the MC during the SNR/MC interaction will be

This value is about 103 times larger than the energy density of the local cosmic rays (where uCR ∼ 0.5 eV cm-3)

a significant CR enhancement of cosmic-ray energy density can be achieved in molecular clouds through their interactions with SNRs.

The number density of ionized particles in a MC environment depends on the ionization rate (due to cosmic rays) a complex recombination process.

The ionization fraction? Assuming ζ scales linearly with the

cosmic-ray energy density

Notice that the ionization rate depends on thenumber density of cosmic rays, rather than the

energy density

Means: Ionization enhancement will decay on a comparably short timescale, as soon as the CR enhancement is removed due to p-p scattering.

What the ionization fraction controls

the ambipolar diffusion rate (and hence the rate of core formation)

1.ONE1.ONE

action of magnetorotational instabilities (MRIs) in circumstellar disks (and hence the rate of disk accretion).

2.TWO2.TWO

ambipolar diffusion rate

1. Standard considerations:the effective diffusion constant D~VA

2 /(γCρ) ∝ ζ-1/2

2. Current observations indicate that the diffusionprocess is too slow to account for the observed statistics ofstarless molecular cloud cores (e.g., Jijina et al. 1999)

this mechanism provides a channel for supernovae to inhibit star formation

MRI

1. disk accretion is produced by an effective viscosity that is driven by turbulence, which in turn is driven by MHD instabilities such as MRI (Balbus & Hawley 1991).

2. In order for MRI to operate, the ionization fractionmust be sufficiently high so that the gas is well coupledto the field

So, cosmic-ray flux can have a substantial impact on disk accretion.

Consider the disk models of Gammie (1996)

The attenuation column densityfor cosmic-ray ionization is ∑0 ≈ 100 g cm-2 (Umebayashi & Nakano 1981).

only the uppermost 100 g cm-2

of the disk can experience enough cosmic-ray ionization for MRI to operate

CR unenhancedCR unenhanced

the disk will experience cosmic-ray ionization down to a larger columndensity ∑* ≈ (1+ln F) ∑0 .

cosmic-ray flux that is enhanced by a factor F

3. The ionization fraction increased with CR flux

2. These cosmic rays can diffuse a distance R ∼ 10 pc into theMC before undergoing p-p scattering leading to catastrophic energy losses.

1. SNRs interacting with MCs can produce substantial enhancement of the flux of CRs in The cloud

4. cosmic-ray enhancement may have a significant impact on star formation processes,

3. CR can inhibit the core formation and accelerateDisk accretion. However, triger SF or not?

2. Should consider the X-ray ionization?

1. The method to estimate CR enhancement is Proper?

If produced via a pion-decay mechanism the gamma-ray luminosity of SNR/MC environments

would peak at the value

η is the fraction of a relativistic proton’s energy that goes into the 0 decay photon channel,

can be estimated using the approximation forthe gamma-ray luminosity due to the decay of

neutral pions